Title: Probability
Author: tarotgal
Fandom: Numb3rs
Rating: G
Pairings: None
Disclaimer: This fandom and its characters do not belong to me in any way, shape or form. I’' just using them to play with for fun.
Summary: Charlie helps out with a bank robbing case, even though he's a bit under the weather.
Author Notes: I wrote this in sections to reflect a television show. And though it's close, it does not follow proper episode rules or script-writing format. I'm definitely not good enough to attempt that! Just call this the simplistic version. Also, I can vouch for the math, but the rest/application is rather made up. Therefore, I apologize if there are any problems with the plot. If anything, it will help you understand why I don't write crime/mystery stories!
Bunny: #7
Feedback: Yes please!

Black boots with high heels step out of a red sports car with state license plates. The woman wearing the boots stepped up over the curve and onto the sidewalk. She walked suavely and steadily towards the backdoor.

A large armored car was pulled up to the bank. And though the several guards on duty looked suspicious to see her, they also looked her up and down. From fishnets under a miniskirt to a sheer top with a dark bra beneath and from raven black hair to deep blue eyes, she was quite the sight.

And so was the revolver she pulled out before they could get to theirs. She smiled pleasantly as she reached into the truck and took out two identical bags filled with money. She fired first and escaped in the car in the middle of the firefight.

Credits Roll

We all use math every day to forecast weather, to tell time, to handle money.
We also use math to analyze crime, reveal patterns, predict behavior.
Using numbers, we can solve the biggest mysteries we know.

Act I: Dinner at the Eppes House

The head of lettuce bounced up and down in the colander as Don held it under the kitchen faucet. He shut off the tap, shook it to drain the water, then handed the whole thing over to his brother. When Charlie did not automatically take it, Don looked up.

Charlie was standing a few feet over at the counter with a bowl in front of him. His eyes were closed and his head was turned such that his nose and mouth were pressed hard into his shoulder. His breathing was silent but came in short, shallow gasps. Finally his body tensed and he sneezed. "ahhhh-Shooo!"

"Gesundheit," Don said, looking curious. "Coming down with something?"

Charlie shook his head. "No," he chuckled. "It's the pepper." He gestured to the several spices he was using.

Don chuckled as well and kept the lettuce extended until Charlie sniffed to clear his nose and took it.

Dinner was nearly complete now, apart from the salad and dressing. The chicken was cooked and the potatoes were boiled and mashed. There was a pan full of double-chocolate brownies cooling as they waited for dessert. The table was set for three, even though there were only two present at the moment. By the time the food was on the table and dished out, however, their father's car could be heard in the driveway.

"Hey!" Alan called in greeting as he walked in the front door. "Didn't start without me, did you?"

"Course not," Don replied, putting his fork down at once. "Why're you so late tonight, Dad?"

Alan walked through the dining room on his way to the kitchen.  "There was a long line at the store," he said, taking a loaf of bread out of the top of the bag in his arms and setting it on the table as he walked past. "Everyone wanted to buy lotto tickets."

"Oh yeah," Don said, nodding and picking his fork up again. "The big drawing's this weekend, isn't it? Don't tell me you bought a ticket, Dad."

"Nah," Alan said from the kitchen with a laugh. He headed back into the dining room and sat down at the head of the table. He took a helping of mashed potatoes and froze, looking at Don. "I bought fifty."

"Fifty!" Don was glad he hadn't just taken a bite. "Dad, do you know how small the chances of winning are? Like one in ten billion."

"Yes, but now they're fifty to ten billion," he said, gesturing with his fork. "Besides, everyone's buying tickets now." He looked over to Charlie for help.

"Actually, Dad, that means there's probably less of a chance of winning. The odds don't change. It's still the same basic equation of odds which comes out to 1 in 254,251,200 at five-factorial, non-replacement of course. Which comes out to 1 in 2,118,760--"

"Did you catch all that, Dad?" Don muttered, hiding a smile. They both knew Charlie was brilliant when it came to these things, and that he loved to explain them as though they all understood it.

"My point is, your odds to increase if you buy more tickets, but the more tickets that are bought, period, decreases your odds of a big payoff slightly. More people matching two, three, or four numbers would decrease the overall pot and it's far more likely to match those then the full five."

Their father cleared his throat. "What you're saying is I shouldn't be calling moving companies and searching for my dream house quite yet, then?"

"I'm afraid not," Charlie said. "But I still wish you... luck..." He turned his head again, directing a strong, sudden sneeze into his shoulder. "hahhhShoo!" His long hair swayed and his nose twitched. He wasn't to be finished with just one. "ahhChoo! ahhhShooo!"

Both his brother and father said "Gesundheit" just as Charlie mumbled "Excuse me."

"You've been sneezing a bit today," Alan said, around his chicken leg. A smile played in his eyes. "Not coming down with something, are you?"

"Of course not." Charlie looked quite uncomfortable at the question.

Alan chuckled to himself. "You wouldn't say even if you were, though. Remember that time you went to school with the flu and a temperature of one hundred and three?"

Charlie looked down at his food and shrugged. "It was the day of the big competition for senior math team. I'd have let everyone down if I'd stayed home. What's staying home in bed to competing in a regional mathematics contest?"

"It's the smart thing to do," Alan answered. "As I recall, you passed out and were rushed to the hospital."

"Yes," Charlie nodded in agreement, remembering, even though the memory was hazy. He looked up, finger held up. "But after I finished the problem set."

Don laughed. "Most kids fake sick to stay home from school. My brother fakes well."

Charlie's reply, however genius it might have been, was overtaken by another sneeze. This one was not quite so sudden. "ahhh..." He had time to grab a napkin out of the holder in the center of the table and fold it over his nose. "ahh-hahh..." He frowned, waiting. Then. "Ahhh-Chhphhh!" The tickle in his nose quickly passed. When he looked up, his father was staring at him critically. Charlie found himself looking at Don for help.

"It's the pepper, Dad," said Don. "At least it had better be, because I think I've got a case at work you could help us out on."

Charlie smiled and gave a nod. "I'd be glad to." In all his excitement, and then the sneezes, he'd barely touched his food. But he dug in now as Don started to explain the case a little.

"Great. It involves this rash of recent bank robberies..."

Act II: Pillow Problems

"All right..." Don said, pacing back and forth in the meeting room in front of the several dozen agents packed in to listen in about the case. His suit jacket had come off earlier that day, his shirt had become untucked, and the sleeves of his dress shirt were unbuttoned and rolled up in a sloppy manner past his elbows. No one batted an eye at it, however. "Here's what we've got so far. The main perpetrator is a woman in her late twenties or early thirties. She changes her appearance each time so we haven't been able to get a good description from any of the witnesses." Don clicked the remote in his hand and the PowerPoint displayed up on the screen in the front of the room cycled through a dozen different shots of the woman in different outfits. "The same thing goes for the getaway car. Every time it's a car that's been stolen that day or the day before. So far we've had no leads when it comes to tracking her down from the cars. No one's seen anything." He clicked through a series of different vehicles.

"How much damage has she done so far?" asked Megan.

"About four million. And eleven dead or injured. Just heard from ballistics and the bullets are far too common to trace. She and her accomplice seem to have inside knowledge about the shipments. We've tried all the normal techniques to throw them off. First we tried sending out some truckloads with bags of fake money, but even when those were stolen, the robbers just tried again during the next shipment anyway. We've checked out the drivers, switched routes, and guarded schedules, but they still show up at the end as though they knew right where it was heading the whole time. And they take two bags."

"Two bags?" Colby exclaimed. "That's all?"

Don nodded. "The only thing that stays the same is that each time she comes onto the scene she leaves with only two bags." He glanced up at the screen as he flipped through security camera pictures of the woman leaving the scenes with a bag in each hand.

At the back of the room, Charlie stood against the wall, arms crossed over his chest. He was listening intently, but also sniffling rather constantly. His mind was racing, though. What Don had just said had triggered something and he was fighting to figure it out.

He noticed the way one of the bags in the many photos always seemed to tilt to the side a bit as she carried it by the handle. Then he realized that was because the bag was slightly broken at the top. Each time. In every picture. "She's carrying the same bag in all of these," he pointed out. He rubbed hard at his nose and sniffed just as hard, knowing everyone in the room was looking in his direction now.

"You're right," said Don, backing those slides up and looking at them again. The bags almost looked identical to each other, but Don suddenly understood they weren't. "The one bag's the same, but the second one is different each time."

David echoed this. "One bag she brings herself, and another she takes from the bank."

"But she doesn't come in with anything," Don said, reviewing the whole set of pictures he had from the cameras to confirm this. "So how does that bag get there each time?"

"This is a pillow problem!" Charlie exclaimed from the back of the room. As all eyes turned towards him, he felt a tickle in his nose. He scrubbed at it, but it rose to the forefront nonetheless. "hahh- ahhChuhh!" He directed it into his sleeve and sniffled liquidly. "Bless me," he said, nearly hidden by his throat clearing. "What I mean is, the robbers are reproducing a classic system called a pillow problem, proposed by Lewis Carroll."

Don's brow furrowed. "Isn't he the guy who wrote Alice in Wonderland?"

Charlie nodded. "That's right. But he also wrote a number of logic problems and mathematical proofs." He took a deep breath, then began to paint a picture of the mathematics with his words. "In this one, he proposed a specific situation in which there is a bag you cannot see through with a stone inside of it. You've got an equal chance that this stone is either white or black. You put a second stone in the bag- a white stone. And what you want, when you pull the stones out, are white stones. Those are the good ones. So you pull one stone out, and it's white. The question is: what are the chances that the other stone inside the bag is white?"

"Isn't it fifty-fifty?" Don replied, not hesitating a bit to answer in front of everyone. "White or black?"

"Not that easy," Charlie replied, rubbing the back of his hand against his nose. He squeezed past a few men and grabbed a whiteboard marker. He scribbled down the possibilities. "If B and W represent your first stone and W2 represents the one you knowingly added... your possibilities are..." His voice died away and he closed his eyes. Facing the whiteboard, he allowed his face to twitch but he tried to keep the build-up relatively silent. He buried his face into his sleeve. "huhh-hahhChhphhh!" He bent forward slightly at the sneeze.

Not wanting his brother to lose momentum, Don jumped back in as soon as Charlie straightened back up. "You could have first pulled out the stone that could have been white or black," he said. "In which case there would still be a white one inside."

Charlie nodded and wrote: OUTSIDE-W INSIDE-W2

"And it could be the other way around," David said.

Charlie wrote beneath that: OUTSIDE- W2 INSIDE-W

Charlie cleared his throat. "And it could have been black," he finished, writing: OUTSIDE-W2 INSIDE-B. "Therefore, if you work it out, it's actually a two-thirds chance that you'll end up with both white. That's significantly better than an even chance."

Don started nodding vigorously. "I see, I see. And you think they're doing this with a truck and bags of money?"

"That's what it looks like to me," Charlie replied. He scribbled an equation on the whiteboard beside the possibilities: 2n/(n+d). "d is the number of bags of money and n is the number that contain real money. By putting in one of their own, they increase the chances greatly of coming out with real money, not bags of fakes. And even if they pick a fake bag, they still get their bag back for sure so they haven't lost anything. They're playing their chances and hoping for the best. If they repeat this method enough, they should come out ahead by a lot. It's governed by probability."

"Like playing more numbers in the lotto," Don muttered. Charlie nodded.

"So how do we decrease their odds?" asked Colby.

"Simple," Charlie said. "The more fake bags you pack into the trucks, the less likely that the criminals will choose a real one."

"Let's make that happen then," Don commanded. "We should also spread word for drivers to look out for this bag they reuse every time. In the meantime, we should keep interviewing witnesses. Someone has to have noticed something else."

The meeting broke up quickly, and Don trusted the others to do their jobs as he headed across the room to see Charlie. The man was standing by the whiteboard still, scrubbing two fingers beneath his nose. Apparently to no avail. His face screwed up and he pitched forward at the waist. "hahh-Shoo! hehhChoo!"

"Picked up a cold after all?" Don asked, crossing his arms over his chest.

Charlie nodded a number of times, shrugging innocently as he did so. He dug a tissue out of his pocket and rubbed at his nose.

"Maybe you should think about heading home--"

"I can't do that," Charlie said quickly. "This might keep them from stealing more real money, but we're no closer to catching them. And I think I can help you out with that." He dabbed at his nose. "Nothing else matters as much as catching these robbers before they can strike again and hurt more people."

"Whatever you can do, would be great, Charlie," Don said, choosing his battles. It wasn't as though Charlie was insisting to go out into the field right now. So long as Charlie did not get too wrapped up in his work that he worked himself up into a typical frenzy, he should be all right.

"Sir?"

Don turned to see David standing there, phone in hand. "We just got a call from the dispatch. Seems one of the armored car drivers has spotted the bag. He's on his way to the bank for his delivery now."

"Tell him to pull over somewhere safe and wait for us. And he shouldn't touch the bag. We'll call the bomb squad in just in case."

Not fifteen minutes later, they were at 32^nd and Beach. The sky was menacingly overcast. As Don got out of the car, he felt a raindrop on his arm and counted his lucky stars that Charlie was back at the office. He definitely did not need to get wet on top of a cold. Besides, it was much safer for him to stay there. The armored car was surrounded by a circle of men with shields and protective gear. "Negative on a bomb, Sir," one of the officers said when Don came on the scene. "But there's definitely something more than money in that bag."

"Thank you," Don said. Flanked by Megan and David who had their guns out just in case. Even though the bag had been brought out, it still looked quite similar to all the others in the truck. Nearly identical, really. If they'd not known any better, they would have thought nothing of the somewhat broken handle. It would have been easy for those loading and unloading to include it. If they were to look inside to decided whether or not to include it or replace its contents, the simplest course of action was just to let it go on ahead, thus playing right into the robbers' hands. Don hesitated a moment, then pulled the bag open.

Beneath the bills in wrappings was a small device the size of a hand. Only a glance at it was enough for Don to know what it was. "This explains why they always showed up in the right place, even with the switches." He picked it up and shook his head as he eyed it. "It's a homing device."

Act III: Predictability

"Really, it made sense that they'd know it was a trap and not show up at the drop-off," David said as they walked back into the office. "The homing device showed the bag was stopped for quite a while and it was hard to miss our presence. Probably scared them off."

"Does that mean they're giving up and we can't rely on a trap to catch them?" Don asked, sounding slightly discouraged. There hadn't been prints on the bag or the money, either. Still, recovering a few hundred thousand was not enough for him.

"I don't think so," Megan said. "Remember what Charlie said about not losing anything in the endeavor? Well, these perps are down a bag now. If they're playing at this for probability's sake, they're going to want to recover their losses from this time. And sooner rather than later."

"So all we have to do now is try to predict where their next hit will be?" Don said as more of a statement than a question.

"I think I might be able to help you there," Charlie interrupted from a nearby desk. He sounded considerably worse- stuffy and deep-voiced. But everyone was more interested to hear what he'd come up with while they were out.

Charlie pulled a large, laminated map over from his desk to the meeting table so they could all gather around it. "You mapped sniff out all the robberies sniffsniff and I've been trying to sniff look for some pattern in order to predict the next one. Sniff! Sniff!" Leaning over as he was, his nose ran more and his sniffling was getting so bad that he could not speak well.

Don looked up and scanned the room. "Hey, Austin!" he called out. "Could you..." He pointed down at the desk. A few moments later, he deftly caught a box of tissues that Austin had tossed over. "Thanks!" he nodded towards the officer. Then he offered the box to his brother.

Charlie did not take them right away, however. Hid face was tense and he had his hand over his mouth, thumb and forefinger pinching his nose. "hahhh-Shoo!" Then he reached for the tissues and took several before burying his nose in them. He snuffled and wiped quickly, then crumpled them up in his hand and cleared his throat. "The strange thing about these plottings is that the events are all over the place and pretty evenly spaced out. What do we know about random events?"

"That they're not evenly spaced?" Don tried.

Nodding and rubbing at his nose again, "That's right. Sniff! There should be spaces and clusters, even if the robbers are trying to be random. But this is a near perfect distribution. Which means... it's not random at all. So I looked at it over time and... and..." He shook his head in frustration. He had just gotten going, only to be stopped. "ahhh-Shoo! hahh-Shooo! hahhhChoo!" He took more tissues and held them to his nose as he continued, sounding more tired as he did so. "There's no pattern at all that governs the other, either. Sniff! They probably just leave the bag somewhere among others, sniff, sniff, and wait for it to be picked up and taken to a bank. So any bank is as equally likely as the next."

"We don't have the resources to stake out every single bank in the area, Charlie."

He continued, "But I did notice that there have been two a week, and no banks have been repeated yet."

"So if they're not making a choice, just going by the schedule... we should look at the next delivery to a bank that hasn't had a delivery for a while?"

Charlie sniffled and nodded. "Chances are good, that's where they'll strike. I can keep crunching the numbers in the meantime, to see if anything else comes up."

"Great. I'll go check the schedules," David said.

"And I'll keep working on trying to track down who might be leaving the bag to be picked up with each shipment," Megan said. "Someone has to have seen something."

The two left, leaving Charlie and Don together again. Charlie straightened, only to snap in half again with another sneeze. "hihhShooo!"

"Gesundheit," Don said, looking sympathetic. "Charlie, we've really got some good leads here. Maybe you should go home and rest."

Charlie shook his head and helped himself to another tissue. "No. There are still a few variables I want to look at. Times of day and the locations of the stolen cars and... and... I'm going to sneeze again. Hold on." He covered his nose and mouth with both hands and the tissues. "ahhhShphhh! ahhhChmphhh!" He blew his nose, swaying slightly, then suddenly lost his balance altogether. He leaned to the side and stumbled as he caught himself before falling.

Don reached out and held him steady. Then he reached up.

Charlie pulled away, a confused look on his face. "What're you doing?"

"I want to check your forehead and see if you're running a fever," Don replied honestly, his hand hanging in mid-air, halfway on its way.

Charlie looked around, feeling self-conscious. "I'd rather you didn't..."

Don laughed. "Come on, Char. It's an older brother's privilege. Quit being a baby." He pressed his hand to Charlie's forehead and frowned as he evaluated.

Charlie waited for a few moments, then grew impatient. "Don?" he asked. Don kept his hand in place, looking thoughtful. "Don?" he repeated, sounding a little more forceful.

Dropping his hand at last, Don nodded. "You're definitely feverish. You should be at home in bed."

Coughing and sniffling accompanied Charlie's headshake. "I've got too much to do. These equations--"

"Can't someone else look at those other variables?" Don asked. "Amita, maybe?" She didn't have security clearance, but since when had that stopped her from helping?

"Don..." Charlie sighed.

Knowing where his brother was going with his, Don tried to head him off. "Look, I know math relaxes you and makes you feel better. Some people watch television, you solve math problems. But this time you really need to be in bed." Charlie hesitated. "Please? I know you love math, but you love me, too, right? Do it for your big brother?"

Finally, reluctantly, Charlie gave in. He nodded. "Yeah, okay. I'll go home and rest for a little while."

"Excellent," Don said with a sigh. "I'll drive you."

"Oh, you don't need to--"

Don laughed. "And have you run into a sign or a parked car or something on your bike because you sneezed at the wrong moment? I don't think so." He fished around in his pocket for his keys and pulled them out. They jangled in his hand as he said, "I'm definitely driving. I could use a break. Come on." He put his arm around his brother and walked Charlie out before the man could change his mind.

Act IV: Pillow Problems Revisited

Charlie leaned forward, snatching several tissues from the box on the coffee table. "ahhh..." He cupped them to his nose as his mouth dropped open for what felt like the thousandth time that day. "hahhShoo! ahhhChooshh!" He snuffled into the tissues. "Dad?" he said, sounding stuffy and coughing. "Could you get be..." Charlie's voice died down as he looked up to see Don standing in front of him, holding a glass of orange juice. Don leaned over the coffee table and handed it over. Charlie took it and took a sip. "Thanks. You read by bide."

Don nodded back. Charlie was stretched out across the whole couch, several blankets draped over him and several pillows on top of one of the couch cushions. Alan sat in the armchair just to the left of the couch. Not wanting to ask either of them to move, Don parked himself on the arm of the chair, half sitting and half leaning, and crossed his arms over his chest.

"Whed'd you get here?" Charlie asked.

"A few minutes ago. Stopped by here on the way home to see how you were doing and to make sure you were resting."

Charlie had another gulp of juice and set the glass down on the coffee table. He coughed several times and rubbed at his nose. He thought about asking what time it was. He thought about asking why Don was here and not at work. But what he really wanted to ask was, "What about the case?"

"We're still working on it. There's a delivery tomorrow morning that seems to fit all the variables you gave us. With any luck, that'll be the one."

"Dot luck," Charlie said, shaking his head. "Brobability." The shake bumped the pillows and caused them to shift so one was down closer to his upper arm. He pushed off from the couch, allowing a moment of space between it and himself where he could push the pillows back up into place. When he laid his head upon them, they still weren't quite right. He punched at them and tilted them and plumped them, trying to get them back to feeling squishy and comfortable again.

"Having pillow problems?" Don joked. He reached over and plumped them for Charlie. "Why is it called that, anyway?"

Charlie settled into them with a smile. "Actually... I'b dot really sure why but baybe... hahh-Chooo!"

"Ah, stalling for time are you?" Don asked, grabbing the tissue box off the table and holding it closer so Charlie wouldn't risk disturbing the delicate balance that was his stack of pillows.

"Hey, Boys, can you keep it down?" Alan asked. "The drawing's about to start." He had the tickets clutched in his hand, and flipped through them as though memorizing the numbers so he'd be able to tell right away if he'd won when the numbers were drawn on TV.

All three of them were silent, apart from some sniffling, as the balls bounced around in the machine. One by one they were caught by the slight suction and rolled through the tube to the opening. A woman in an appropriately green dress turned them as needed to face the camera.

Alan jotted down the numbers as they were announced, then quickly shuffled through his tickets. Charlie and Don watched with rapt attention.

"So Dad, did you win?" Don asked finally, looking down over his father's shoulders what tickets he could see.

Alan sighed deeply and shook his head. "This ticket," he said, holding one up. "This matched two. But that's the only one."

"And what's the payoff for two?"

"Fifty dollars," he replied slowly, sounding somewhat mystified. "Ha! I broke even! What are the chances of that?"

Charlie perked right up and cleared his throat. "Actually, they're--"

Laughing, both Alan and Don jumped in with hands up and eyes wide, warning him not to answer if he wanted to keep his comfy position on the couch.