A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 8 18 17 43Female 15 5 10 30Total 23 23 27 73If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got an 'A'.
Question
A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 8 18 17 43Female 15 5 10 30Total 23 23 27 73If one student is chosen at random from those who took the test,Find the probability that the student was female GIVEN they got an 'A'.
Solution
To find the probability that a student was female given they got an 'A', 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 an 'A'.
From the table, we can see that:
- The total number of students who got an 'A' (P(B)) is 23.
- The number of female students who got an 'A' (P(A ∩ B)) is 15.
Substituting these values into the formula, we get:
P(A|B) = P(A ∩ B) / P(B) = 15 / 23 = 0.652
So, the probability that a student was female given they got an 'A' is approximately 0.652 or 65.2%.
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