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)
Mathematics · High School · Tue Nov 03 2020
Answered on
(a) P(A ∩ B) = P(A)P(B)
=0.35*0.25 = 0.0875
(b) P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
= 0.35+0.25-0.0875 = 0.5125
(c) P(A | B) = P(A ∩ B)/P(B)
= 0.0875/0.25 = 0.35
(d) P(Ac ∪ Bc) = P(Ac) + P(Bc) - P(Ac ∩ Bc)
= P(Ac) + P(Bc) - P(Ac)P(Bc)
= 1 - 0.35 + 1 - 0.25 - (1 - 0.35)(1 - 0.25)
= 0.65 + 0.75 - 0.4875 = 0.9125