Question

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

	A	B	C
Male	8	11	6
Female	5	17	18

A) If one student is chosen at random from those who took the test, find the probability that the student got a 'A' given they are female.  

Round your answer to three decimal places.  

B) If one student is chosen at random from those who took the test, find the probability that the student is a female given got a 'A' .  

Round your answer to three decimal places.  

Answer 1

a)

Total number of females who gave the test = 5+17+18=40

Total number of females who got A in the test = 5

so the probability that a student got A given that she is a girl is = 5/40=0.125

b)

Now to find the probability that the student is a female given that it got a A

So total number of students who got A = 8+5=13

Total number of females who got A = 5

so the probability that the student chose who got a A is a female is = 5/13=0.385

Thank you !!