Question

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

	a	b	c	total
female	15	13	14	42
total	19	30	19	68

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 c. round answer to three decimal places.

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 'C'. Then $P(A|B)=\frac{n(A\cap B)}{n(B)}$, where $n(A\cap B)$ is the number of male students who got a 'C' and $n(B)$ is the total number of students who got a 'C'.

Step2: Identify values from the table

From the table, $n(A\cap B)$ (number of male students who got a 'C') is 5, and $n(B)$ (total number of students who got a 'C') is 19.

Step3: Calculate the probability

$P(A|B)=\frac{5}{19}\approx 0.263$

Answer:

$0.263$