in a class of 24 students, 17 are female and 8 have an a in the class. there are 5 students who are female…

in a class of 24 students, 17 are female and 8 have an a in the class. there are 5 students who are female and have an a in the class. what is the probability that a student is a female given that they have an a?

in a class of 24 students, 17 are female and 8 have an a in the class. there are 5 students who are female and have an a in the class. what is the probability that a student is a female given that they have an a?

Answer

Answer:

$\frac{5}{8}$

Explanation:

Step1: Recall conditional - probability formula

$P(A|B)=\frac{P(A\cap B)}{P(B)}$ In the context of this problem, let $A$ be the event that a student is female and $B$ be the event that a student has an A. $P(A|B)$ is the probability that a student is female given that they have an A.

Step2: Identify relevant numbers

The number of students who have an A is $n(B) = 8$. The number of students who are female and have an A is $n(A\cap B)=5$.

Step3: Calculate the probability

$P(A|B)=\frac{n(A\cap B)}{n(B)}=\frac{5}{8}$