Chapter 11
BAYES’ THEOREM
JAHLANI
“Alright, so today we’re going to talk about conditional probability and Bayes’ Theorem.”
Jahlani pushes her braids behind her ears, walking around the room. “Everything was put online. You had a whole weekend to look over it and ask questions.”
“Professor Jackson didn’t upload anything,” someone calls from the back.
Jahlani scratches her nose, moving to her laptop. “You sure?”
“There was nothing, Ms. Jones.”
She rolls her eyes. “It’s Jahlani. Just Jahlani,” she repeats under her breath as she clicks through the course landing page.
After the first few days, Jackson saw an influx of students.
He came up with the idea for them to split the class in half.
Every week, a set portion would move to a different room with her while the others would stay back with him.
She didn’t expect to be teaching, teaching, but he has the type of authority that you don’t question, and she likes the challenge.
Some deep, dark part of her wants to prove herself to him.
“It’s fine,” she announces, facing them. “We’ll just have to do double the work today.”
Moving to the whiteboard, she writes the equation.
“Okay, let’s look at the formula first. This is called posterior probability.
All it means is this—” She continues speaking as she writes.
“The probability of A happening given that B has already occurred. It’s an equation allowing one to find the probability of a cause given its effect. Are you with me so far?”
She turns toward the students, seeing a scattered wave of nods.
“Amazing. Let’s break this down further.”
Moving to the opposite side of the board, she sketches a box with arrows.
“These arrows”—she points to them—“represent conditional relationships.” She snaps the cover on the marker. “Okay, someone give me a pizza topping they hate.”
“Pineapple!”
“Okay, whoever said that, you’re not passing this semester.”
A few chuckles wave throughout the room and she feels warm at the reaction.
“So, here’s an example of how this theorem works at the surface level.
Let’s say you’re at a party. At this hypothetical party, you know that people who like pineapple on pizza are more likely to be from Florida—remember this is hypothetical,” she adds when a series of gasps and gagging sounds are heard across the room. She waits for everyone to settle.
“Okay, let’s change the example since we hate the pineapple one so much,” she says, as scattered applause starts.
“Let’s stick with pizza, but now it’s a deep dish. At this party, we know that people who like it are more likely to be from Chicago. So, the fact that someone is from Chicago makes it more likely they’ll like deep-dish style pizza.”
She pauses, waiting for questions. When none come, she presses on. “Now, if we know that an individual likes deep dish, we have to ask ourselves, how does that change our belief that they’re from Chicago? That is something that Bayes’ Theorem will help us calculate.”
Turning back to the board, Jahlani draws an arrow between the two factors, labeling them.
“So, P(A|B) is the probability that they are from Chicago, given that they like deep dish. And P(B|A) is the probability that someone from Chicago likes deep dish.
“So, maybe you start with some prior belief about deep dish preferences—say, sixty percent of people like it. But then, you learn someone’s from Chicago. Bayes’ Theorem lets you update your belief about whether they like deep dish.”
She turns back and waits for students to write and type the information down.
The door swings open, and she does a double-take.
Her thoughts stutter for a moment because he’s here in another long-sleeve that is doing a lot for his biceps, and doing everything for her body.
She lingers as she watches him move up the stairs swiftly, settling into the third row, second seat in. The same every time.
She’s suddenly irritated that she’s memorized where he sits. What a useless piece of information, she thinks, and turns away from his frame, shaking the very detailed images of what she thinks his arms look like underneath from her mind.
She clears her throat. “Sorry, what was I saying?”
Looking back at the board, she drops the marker, wiping clammy hands on her sides.
“You were telling us the purpose of Bayes’ Theorem,” a voice rings out near the front.
Right. Bayes’ Theorem.
She nods, picking up her water bottle and taking multiple sips. Setting it down, she moves back to the center, trying, and failing, not to look his way every three seconds.
The rules. Stick to the rules.
“Okay,” she says, stepping back. “Let’s work through an example together. I want everyone to pair up. I’ll give you a scenario, and we’ll apply Bayes’ Theorem to figure out how likely someone is to have a certain trait, based on new evidence.”
She hands out printed scenarios, and student murmurs fill the air.
Jahlani weaves around the room, helping here and there, but mostly letting the students work through the math themselves.
From the corner of her eye, she watches Roman drum his fingers on his laptop. She hesitates before moving toward him.
Forest green eyes meet hers, and she tries to keep her face as neutral as possible.
“Hi,” he says, sitting upright in his seat, flooding her with a slow smile.
She moves her braids back over her shoulders, and he tracks the movement, his nostrils flaring.
“Nice of you to show up,” she says, trying to rein back her sharp tone.
He runs his pen across his lips, and she clears her throat, looking around the room as her body flushes.
“I know, I know,” he says, shifting in his seat. “Catch me up?”
She scoffs, facing him. “Hate to break it to you, Roman, but that’s not how this works. I have other students to help. Don’t be lazy. Get here on time.”
He runs a hand through his hair, rubbing the back of his neck.
“I had a situation,” he says, his voice lower this time, eyes dimmer. “And, I thought you said you would help.”
She crosses her arms over her chest. Leaning forward, she speaks in a low voice.
“I agreed to help someone who actually wants help, not someone who picks when to show up and half-asses things. If you want to pass this class and graduate, take it seriously.”
His head rears back. “I am.”
She straightens up, wrapping her braids into a high ponytail.
“No, you’re not,” she says, shaking her head and pursing her lips. “This is week two, and you’ve been late to almost every lecture. You completely bombed the last quiz. I can’t help someone who doesn’t want to be helped. That isn’t putting in any effort.”
He frowns, and she wonders if she came off too harsh. “Jahlani, I had a family situation.”
She freezes, then lowers her gaze to the ground.
Always quick to assume the worst about people now.
“Shit,” she breathes, shaking her head. “I’m sorry. Is everything alright? Did someone …” She trails off, not wanting to finish that thought, not wanting to be insensitive. Or at least even more so than she already has been.
His lips turn upward as he looks at her, and her pulse races. “Nobody died, if that’s what you’re thinking, and it’s okay. It happens to the best of us. First impressions matter, and I haven’t made the best one on you, I guess.”
Her eyes soften as she chews her lip. He’s so pleasant.
It pisses her off.
“Look,” she says, releasing a slow exhale. “If you want help, office hours are every Tuesday and Thursday. I’m pretty much there the whole day. I also … linger around after class for a few hours, but don’t broadcast that to anyone.”
Jahlani walks away before he can say anything. Returning to the front, she turns her mic on again.
“Alright, let’s go over the answers together.”
For the next half hour, she works writing the different solutions onto the board, addressing misconceptions, keeping her tone airy and relaxed, encouraging students to share and discuss.
The whole time, the nape of her neck prickles as he watches her.
Only her. Every now and then he checks his phone, smiles at something that makes her curious, writes things down in his notebook, but his gaze never leaves her form.
It’s good, she thinks. It means he’s paying attention. That’s all.
“Remember, Bayes’ Theorem isn’t just for parties and pizza; it’s used in everything from artificial intelligence to risk management. Keep practicing, and you’ll start to see it everywhere.”
He watches for an unnerving amount of time as students begin to gather their belongings, and she knows she was too harsh on him earlier.
She just doesn’t know why.
A tiny part of her thinks that he genuinely wants the help, and that other part of her, the part that’s been burned too many times, thinks that he didn’t mean what he said that day and he’s just playing her like a fool.
“Before you leave for the day, a reminder about the Graduate Affairs Event for Data Science and Statistics next Friday. Jackson has promised extra credit for students who attend and stay for at least thirty minutes. We will be there the whole time to verify attendance.” She meets viridescent eyes from across the room as she speaks the next few words.
“I encourage you all to come out. Especially those of you who didn’t do so well on our first quiz.
It won’t save your grades, but it will definitely help in the long run. ”
She checks the time on her watch.
“That’s all I have for today. I’ll be around for a few minutes for any lingering, life-altering questions that need to be answered. Otherwise, I’ll see you all again on Friday.”
Jahlani waves goodbye to students while she collects her things. As the auditorium empties, she places her laptop, along with her charger, into her bag.
A familiar lavender scent hits her, and her hands start to tremble—her body reacting to his presence before her mind can gather coherent, safe thoughts.