Final answer:
To calculate the probability that a student has an A given that the student is female, divide the number of female students with an A by the total number of female students, which gives a probability of 0.8 or 80%.
Step-by-step explanation:
In order to find the probability that a student has an A given that the student is female, we can use the concept of conditional probability. We are told there are 15 female students and 12 female students who have an A. Using the formula for conditional probability, P(A | F), where P(A) is the probability of having an A, and F is the event that the student is female, we can calculate this probability.
The probability that a student has an A given that the student is female is found by:
P(A | F) = P(A AND F) / P(F), where P(A AND F) is the probability of being female and having an A, and P(F) is the probability of being female.
P(F) = number of female students / total students = 15/25
P(A AND F) = number of female students with an A / total students = 12/25
Substituting these values into the equation gives:
P(A | F) = (12/25) / (15/25) = 12/15 = 0.8
Therefore, the probability that a student has an A given they are female is 0.8 or 80%.