If A and B are independent events PA 015 and PB 065 find t

If A and B are independent events, P(A) = 0.15, and P(B) = 0.65, find the probabilities below. (Enter your answers to four decimal places.)

(a)    P(A ? B)

(b)    P(A ? B)

(c)    P(A | B)

(d)    P(A^c ? B^c)

Solution

a) Since the events A and B are independent, according to the Multiplication Theorem of Probability
P(A and B) = P(A)*P(B)
= 0.15*0.65
= 0.0975

b) I think the question is P(AUB)
According to the Addition Theorem of Probability
P(AUB) = P(A)+P(B)-P(A and B)
= 0.15+0.65-0.0975
= 0.7025

c) P(A | B) = P(A and B) / P(B)
= 0.0975 / 0.65 = 0.15 because the events are independent

d) P(Ac and Bc) = P(Ac)*P(Bc)
= (1-P(A))*(1-P(B))
= (1-0.15)*(1-0.65)
= 0.85*0.35
= 0.2975