A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 20 14 19 53Female 5 12 17 34Total 25 26 36 87If one student is chosen at random from those who took the test, find the probability that the student got a 'a 'C'' GIVEN they are male. Write your answer as a reduced fraction.P(C ∣∣ male) =
Question
A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 20 14 19 53Female 5 12 17 34Total 25 26 36 87If one student is chosen at random from those who took the test, find the probability that the student got a 'a 'C'' GIVEN they are male. Write your answer as a reduced fraction.P(C ∣∣ male) =
Solution
To find the probability that a student got a 'C' given they are male, we need to use the formula for conditional probability which is P(A|B) = P(A ∩ B) / P(B).
Here, event A is that the student got a 'C' and event B is that the student is male.
From the table, we can see that the number of male students who got a 'C' (which is the intersection of A and B) is 19. The total number of male students is 53.
So, P(C ∩ male) = 19/87 (the ratio of male students who got a 'C' to the total number of students)
And P(male) = 53/87 (the ratio of male students to the total number of students)
Substituting these values into the formula gives us:
P(C|male) = (19/87) / (53/87) = 19/53
So, the probability that a student got a 'C' given they are male is 19/53.
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