Question

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 19 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.

1.A randomly selected passenger went rock climbing, given they did not go ice skating

2. A randomly selected passenger did not go rock climbing, given they did not go to the fitness center

3.A randomly selected passenger did not go ice skating, given they did at least two activities

Draw a Venn Diagram for the three sets if necessary. Include how you found the number of ALL three activities.

Answer 1

Here the probability to find are the conditional probabilities.

Let I be the event that person went Ice skating

Similarly R for rock climbing

F for fitness centre

1) The probability that a randomly selected passenger went rock climbing, given they did not go ice skating

There is a total of 86 passengers

2) The probability that A randomly selected passenger did not go rock climbing, given they did not go to the fitness center