Fiction Cruiseline offers three ways to exercise on their cruise ships. 73 of the 86 passengers participated in at least one method of exercise. 36 people went rock climbing, 44 people went ice skating, and 27 went to the fitness center. 14 people went rock climbing and ice skating, 11 people went rock climbing and to the fitness center, and 9 people went ice skating and to the fitness center. Calculate the probability for each given event.

The probability of exercise in cruise ships = 73

Step-by-step explanation:

Let A be the probability of rock climbing

Let B be the probability of ice skating

Let C be the probability of fitness center

P(A) = 36, P(B) = 44, P(C) = 27

P(A ∩ B) = 14, P(A ∩ C) = 11, P(B ∩ C) = 9

P(A ∩ B ∩ C)=0

By formula,

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − P(A ∩ B) − P(A ∩ C) − P(B ∩ C) + P(A ∩ B ∩ C).

Substituting the values in the above formula,

P(A ∪ B ∪ C) = 36 + 44 + 27 - 14 - 11 - 9 + 0

  = 107 - 14 - 11 - 9

P(A ∪ B ∪ C)  = 73

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