Question

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

	a	b	c	total
female	18	4	9	31
total	20	23	19	62

if one student is chosen at random from those who took the test,
find the probability that the student got a c given they are male.
question help: video message instructor

Explanation:

Step1: Identify relevant values

We want $P(\text{C}|\text{Male})$. The number of male students is 31 (total in male - row). The number of male students who got a 'C' is 10.

Step2: Apply conditional - probability formula

The formula for conditional probability $P(A|B)=\frac{P(A\cap B)}{P(B)}$. In terms of counts, $P(\text{C}|\text{Male})=\frac{\text{Number of male students with 'C'}}{\text{Total number of male students}}$. So $P(\text{C}|\text{Male})=\frac{10}{31}$.

Answer:

$\frac{10}{31}$