there are 28 students in a class, 12 boys and 16 girls. an experiment involves choosing two students at random from the class. let A be the event: "the first chosen is a girl" and B the event "the second chosen is a boy." a) find P(A) and P(B) and P(A\B)

To calculate the probabilities for the events A and B, we can use the concepts of conditional probability and the total number of students in the class. Let's break it down step by step: Total number of students = 28 Number of boys = 12 Number of girls = 16 a) Find P(A) (the probability that the first chosen student is a girl): P(A) = (Number of girls) / (Total number of students) P(A) = 16 / 28 P(A) = 4 / 7 b) Find P(B) (the probability that the second chosen student is a boy): Since the first student has already been chosen, the total number of students remaining is 27. And the number of boys remaining is 12 (since one girl has been chosen as the first student). Therefore: P(B) = (Number of boys) / (Total remaining students) P(B) = 12 / 27 P(B) = 4 / 9 c) Find P(A ∩ B) (the probability that both the first chosen student is a girl and the second chosen student is a boy): Since the first student chosen is a girl, there are 16 girls left and 12 boys in the class. Therefore: P(A ∩ B) = (Number of girls) / (Total remaining students) * (Number of boys) / (Total remaining students - 1) P(A ∩ B) = (16 / 27) * (12 / 26) d) Find P(A|B) (the probability that the first chosen student is a girl, given that the second chosen student is a boy): P(A|B) = P(A ∩ B) / P(B) Now you have the probabilities for events A, B, and A ∩ B. Just substitute the values and perform the calculations to get the specific probabilities.