A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 13 18 2 33Female 15 7 12 34Total 28 25 14 67If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got a 'B'.
Question
A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 13 18 2 33Female 15 7 12 34Total 28 25 14 67If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got a 'B'.
Solution
To find the probability that a student was female given they got a 'B', 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 is female and event B is that the student got a 'B'.
From the table, we can see that:
- The number of students who got a 'B' (event B) is 25.
- The number of female students who got a 'B' (the intersection of events A and B) is 7.
So, the probability that the student was female given they got a 'B' is:
P(A|B) = P(A ∩ B) / P(B) = 7 / 25 = 0.28
So, the probability is 0.28 or 28%.
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