“Let’s say that the probability of a first-year student contracting an STI is 5 percent.”
The groans stopped. Replaced by a solitary uncomfortable chuckle. Ivy, worried that her resolve would fade, kept her eyes locked on the screen. She scribbled: “STI probability = 5%.”
Her penmanship was horrible.
“Now, let’s say you were a bit... concerned after a particularly eventful weekend. You decide to get tested. The test isn’t perfect—they rarely are. Now, if youhavean STI, the test is fairly accurate—95 percent of the time, it will come back positive. But if you don’t actually have an STI, the false positive rate is 10 percent.”
She wrote these numbers on the board, too.
No laughs now; no groans, either.
A good sign? Were they finally following along? Or just too shocked to react?
Ivy still couldn’t believe that she was going through with this. The lasting effects of alcohol were still lowering her inhibitions.
Had to be.
“Hypothetically, after your weekend, the test comes back positive. What are the chances that you have an STI?”
Ivy finally raised her eyes. She was surprised to see everyone’s attention locked on the display. Everyone except Zeke, because Ivy still couldn’t bring herself to look at him.
“Anyone?”
“95 percent?” someone offered.
And that’s why you guys bombed the first test.
“Not quite. Don’t freak out just yet. Here’s Bayes’s formula.”
P(A|B)= P(B|A)⋅P(A)
P(B|∼A)⋅P(∼A)+ P(B|A)⋅P(A)
“Where P(A) is equal to the probability that someone in first year has an STI—so 5 percent. P(B|A) is the opposite, that youdon’thave an STI—95 percent. P(~A) is the true positive rate of the test—also 95 percent. While P(B|~A) is the false positive rate—people who don’t have an STI but still test positive—10 percent.”
Ivy was on a roll now, writing at a rapid clip. Penmanship still awful.
“Now, to find the actual probability that you have an STIandtested positive, all we have to do is run the numbers.”
The math was fairly simple, and Ivy had no problem performing the calculations even with her foggy brain. She wrote out all the steps, then circled the final value.
≈0.333.
“So? What’s the answer?”
A beat of silence.
Ivy was worried that she’d lost them somewhere along the way. Not sure how, given how simple her example was. Simple and relatable.
Then someone said, “It means that Zeke might not have gonorrhea!”
The class erupted into laughter.
Try as she might, Ivy found it impossible to keep from smiling.
“It means that you should always double bag it in first year!”
“Yeah, I think the horse has already left that barn on that one,” Ivy said.
