A travel agency books holiday tours to Italy, Greece, and other countries in Europe. A supervisor notes that the probability tha
t a client visits Greece on a tour is 0.28, and the probability that a tour includes Italy is 0.55. The probability that a client visits both Greece and Italy on the same tour is 0.11. What is the probability that a client chooses Greece, or Italy, or both countries, on a tour?
Let A represent the event that a client chooses to visit Italy on a tour. Let B represent the event that the client chooses to visit Greece. As a client may visit both countries on the same tour, the events A and B are not mutually exclusive.
P(A or B) = P(A) = P(B) - P(A and B) = 0.55 + 0.28 - 0.11 = 0.72
So the probability that a client chooses Greece, or Italy, or both countries, on a tour is 0.72.
P(Greece) =0.28 among tem P(G∩I) = 0.11. We also know tat P(G ∪ I ) =1 [either Greece or Italy or both= all travelers) The only data that is missing is te P(Italy) P(G ∪ I ) = P(G) + P(I) - P(G∩ I) 1 =0.28 + P(I) so P(I) = 0.72 P(G) = 0.28 (including the 0 .11) P(I) = 0.72 (including the 0.11) P(G and I) =0.11
