Question

aIn a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student is amale given that they have an A?Female MaleHas an A42Does not have an A167-

Answer 1

Solution

We have the following info given:

Female Male

Has an A 4 2

Dos not have an A 16 7

And we want to find the probability that a student is a male given that they have an A?

We can create this notation:

M= student is male

A= student have an A

So we want this: P(M|A) and we can use the following formula using the conditional probability rule:

$P(M|A)=\frac{P(\text{MandA)}}{P(A)}$

And we can find the probabilities:

P(M and A) = 2/29

P(A)= 9/29

And replacing we got:

$P(M|A)=\frac{\frac{2}{29}}{\frac{9}{29}}=\frac{2}{9}$