Question

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

A B C Total
Male 12 15 4 31
Female 9 8 16 33
Total 21 23 20 64
If one student is chosen at random, find the probability that the student was male GIVEN they got a 'C':

Answer 1

To find the probability that the student was male given they got a 'C', we need to use Bayes' theorem. Bayes' theorem states that:

P(A|B) = P(B|A) * P(A) / P(B)

where P(A|B) is the probability of event A given event B, P(B|A) is the probability of event B given event A, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.

In this case, event A is "the student is male" and event B is "the student got a 'C'". We are given the following information:

- P(A) = 31/64 (the prior probability of a student being male)
- P(B|A) = 4/31 (the probability of getting a 'C' given the student is male)
- P(B) = 20/64 (the prior probability of getting a 'C')

Using Bayes' theorem, we can calculate P(A|B) as:

P(A|B) = P(B|A) * P(A) / P(B)
P(A|C) = (4/31) * (31/64) / (20/64)
P(A|C) = 4/20
P(A|C) = 0.2

Therefore, the probability that the student was male given they got a 'C' is 0.2 or 20%.

Answer 2

Answer:
`(1)/(5)`

Explanation:

Males who got a C = 4

Total amount of people who got a C = 20

`(4)/(20)`

`(4)/(20)` simplifies to
`(1)/(5)`