A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 3 19 13 35Female 14 2 17 33Total 17 21 30 68If one student is chosen at random from those who took the test,Find the probability that the student got a 'C' GIVEN they are male.
Question
A test was given to a group of students. The grades and gender are summarized belowA B C TotalMale 3 19 13 35Female 14 2 17 33Total 17 21 30 68If one student is chosen at random from those who took the test,Find the probability that the student got a 'C' GIVEN they are 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 total number of students who are male and got a 'C' (P(A ∩ B)) is 13.
- The total number of male students (P(B)) is 35.
Substituting these values into the formula gives us:
P(A|B) = P(A ∩ B) / P(B) = 13 / 35 = 0.3714
So, the probability that a student got a 'C' given they are male is approximately 0.3714 or 37.14%.
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