Question

giving a test to a group of students, the grades and gender are summarized below

	a	b	c	total
female	11	19	18	48
total	13	28	32	73

if one student is chosen at random, find the probability that the student was male given they got a b. type as a fraction.

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Explanation:

Step1: Recall conditional - probability formula

The formula for conditional probability is $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts from the table, if $A$ is the event of being male and $B$ is the event of getting a 'B', then $P(A|B)=\frac{\text{Number of male and B}}{\text{Number of B}}$.

Step2: Identify relevant values from the table

The number of male students who got a 'B' is 9. The total number of students who got a 'B' is 28.

Answer:

$\frac{9}{28}$