A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 15 7 14 36Female 11 5 2 18Total 26 12 16 54If 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 15 7 14 36Female 11 5 2 18Total 26 12 16 54If 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' (P(B)) is 12.
- The number of female students who got a 'B' (P(A ∩ B)) is 5.
Substituting these values into the formula gives us:
P(A|B) = P(A ∩ B) / P(B) = 5 / 12 = 0.4167
So, the probability that a student was female given they got a 'B' is approximately 0.42 or 42%.
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