Question

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

	A	B	C	Total
Male	6	15	12	33
Female	9	14	2	25
Total	15	29	14	58

If one student is chosen at random,

1. Find the probability that the student was female:    
2. Find the probability that the student was female AND got a "A":    
3. Find the probability that the student was female OR got a "A":    
4. If one student is chosen at random, find the probability that the student was female GIVEN they got a 'A':    

Answer 1

Problem statement: A test is being conducted among a group of students. Gender and grades obtained are provided in a table. Based on the information in the tase, we have to answer the questions.

Given : A summary table of 58 students with their grades obtained along with the gender.

Problem (A): Compute the probability that student was a female.

Probability = (number of female students)/(total number of students)= 25/58=0.43

Problem(B) : Compute the probability that the student was female AND got a "A".

From the table number of female students who got an "A" is 9.

Probability = (number of female students who got an "A")/(total number of students)= 9/58=0.155

Problem(B) : Compute the probability that the student was female OR got a "A".

From the table we observe number of female students=25 -(1)

number of students getting "A" irrespective of gender= 15 - (2)

Number of female students who got an "A" grade= 9. -(3)

Since these 9 students are included in both (1) and (2), we have to avoid them getting counted twice while computing probability.

So to get actual number of students who was female OR got a "A", we have to use the calculation,

Number of female students OR got a "A" is (1)+(2)-(3)= 25+15-9=31

Total number of students who are either female or got "A" is 31.

Probability that a student chosen at random is female or got "A" is : ( Total number of students who are either female or got "A")/(Total number of students)= 31/58=0.5344.

Problem (D) : Now since that it is given that the student is a female, our sample space changes from 58 students to 25 students

Probability that student got an "A", given that student was a female= (number of female students who got an "A") /(total number of female students)=9/25 = 0.36 .