If P(G) = 0.42, P(H) = 0.59, and P(G ∩ H) = 0.13, find the following probabilities:

Question

4. If P(G) = 0.42, P(H) = 0.59, and P(G ∩ H) = 0.13, find the following probabilities:

(a) P(G ∪ H) =

(b) (4 points) P(Gc ∪ Hc) =

(c) P(Hc ∩ G) =

d) P(Hc|G) =

Answer 1

4. If P(G) = 0.42, P(H) = 0.59, and P(G ∩ H) = 0.13, find the following probabilities:

(a) P(G ∪ H) = P(G) + P(H) - P(G and H) = 0.42 + 0.59 - 0.13 = 0.88

(b) (4 points) P(Gc ∪ Hc) = P(Gc) + P(Hc) - P(Gc and Hc) = P(Gc) + P(Hc) - (1 - P(G and C)) = 0.58 + 0.41 + (1 - 0.13) = 0.99 - 0.87 = 0.12

(c) P(Hc ∩ G) = P(G) - P(H and G) = 0.42 - 0.13 = 0.29

d) P(Hc|G) = P(Hc and G)/P(G) = 0.29/0.42 = 0.69