Statistic question

Question

The probability that Lisa passes her math class is 0.65, the probability that she passes her english class is 0.75, and the probability that she will pass her math class given that she passes her english class is 0.8. Find the probability that she will pass

(a) both of her classes.

(b) neither one of her classes.

Answer 1

Event A = pass math class

Event B = pass English class

P(A) = 0.65

P(B) = 0.75

P(A|B) = 0.8

a) P(A and B) = P(A|B)*P(B) = 0.8 * 0.75 = 0.6

b) P not(A or B) = 1 - P(A or B) = 1 - (P(A) + P(B) - P(A and B)) = 1 - (0.65 + 0.75 - 0.6) = 1 - 0.8 = 0.2