Question

a test was given to a group of students. the grades and gender are summarized below.

	a	b	c	total
female	19	7	2	28
total	31	23	13	67

if one student is chosen at random from those who took the test, find the probability that the student was male given they got a b. round answer to three decimal places.
0.239 ×

Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In the context of this problem, let $A$ be the event that the student is male and $B$ be the event that the student got a 'B'. Then $P(A\cap B)$ is the probability that a student is male and got a 'B', and $P(B)$ is the probability that a student got a 'B'.

Step2: Calculate $P(A\cap B)$

The number of students who are male and got a 'B' is 16. The total number of students is 67. So $P(A\cap B)=\frac{16}{67}$.

Step3: Calculate $P(B)$

The number of students who got a 'B' is 23. The total number of students is 67. So $P(B)=\frac{23}{67}$.

Step4: Calculate $P(A|B)$

Using the conditional - probability formula $P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{\frac{16}{67}}{\frac{23}{67}}=\frac{16}{23}\approx0.696$.

Answer:

$0.696$