I have my notebook in my hand already. I unzip the front pocket of my bag and pull out the loose graded pages. The first quiz, which I got back on Friday, says 71 in red ink at the top. The first homework, which I got back yesterday, says 64. I am, briefly, considering not handing them over. I could tell her that I forgot them and request a new tutor. After all, there’s clearly a reason my sister has been hiding this girl.
I look at the papers and then hand them over. She takes it and looks at the quiz. Nothing in her face changes, and I don’t know why I expected it to. She turns it over, and then she looks at the homework. She’s looking at each answer quietly.
It’s forty seconds of silence. I don’t know what to do with my hands. I wipe them on my pants, stare at the table, and then look back at her. I shouldn’t stare, so I look at the paper in her hands. Shit, that’s still staring, isn’t it? If I can notice that her sweater is made of wool and hangs on one side, then yeah, that’s fucking staring. I glance down at the pencil she had in her mouth, noting the bite marks on it. My knee starts bouncing.
“Okay,” she says finally. “I see what’s happening.”
I stop bouncing my knee. This is good news. “Yeah?”
She says, “You understand the concept. You don’t understand the notation.”
I am, briefly, dumb. “Okay.”
She slides the homework paper across the table to me. She points with the eraser end of her pencil, and I can’t stop staring at the teeth marks.
“This question. You answered the joint probability. The question is asking for the conditional probability. You did the math right. You did the wrong math right.”
I look at where she is pointing. The problem says,Given that the patient tested positive, what is the probability that they have the disease,and underneath it is my work, which is — I can see it now, looking at it with her finger near it — the probability of a positive testandthe disease, calculated correctly to four decimal places. Wrong question. Right math. I read the problem one more time.
“Oh,” I say.
“Yeah. You’re answering the question you think it’s asking. The question it’s actually asking is not the same question.”
“I — okay.”
She touches the blue notebook to her right and slides it across the table toward me. It has a piece of blue tape with my name written in Sharpie across the front. She has good handwriting.
“This is yours,” she says, like it’s not a big deal, but I didn’t know tutors buy their students supplies. I stare at my name written on blue tape. “We’re going to go problem by problem. I’ll read each one out loud, and you’re going to tell me what you think it’s asking. Then I’m going to tell you what it’s actually asking. Your problem is not the math. Do you have your textbook?”
I pull it out and place it in front of me.
“Good. Open your notebook to a fresh page. Number the lines one through five. We’re starting with the homework you just got back.”
I open the notebook and number the lines one through five. I pick up a clean pencil.
The first problem is a conditional probability problem about whether somebody owns a dog given that they own a cat. The numbers in the problem are slightly insane — sixty-one percentof households surveyed own at least one pet, of which forty-two percent own a cat, of which — by the time she has read it aloud once I have already lost track.
“Read it again,” I say.
“Sure.” She reads it again. Her voice is the same flat, even, professional voice she has been using since I sat down.
“Okay,” she says. “What is the question asking for?”
“Probability of a dog given a cat.”
“Right. So which probability is that?”
“Conditional.”
“Yep. So what do we need?”
“P of dog given cat.”
“Which is?”
I have to look at the textbook. She waits.
“P of dog and cat over P of cat.”
