If a and b are independent events, p(a) = 0.25, and p(b) = 0.45, 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(ac ∪ bc)

we are given two probabilities of two events:  P(A) = 0.25, and P(B) = 0.45. we are asked to determine  P(A ∩ B) which has a formula of P(A) * P(B) equal to 0.25 *0.45 equal to 0.1125.  P(A ∪ B) has a formula of P(A) + P(B) equal to 0.70. (c) P(A | B) is 0.25/0.45 equal to 0.56. (d) P(Ac ∪ Bc) is equal to (1-0.25)*(1-0.45) equal to 0.4125.