A study by the National Park Service revealed that 50 percent of vacationers going to the Rocky Mountain region visit Yellowstone Park, 40 percent visit the Tetons, and 35 percent visit both. a. What is the probability a vacationer will visit at least one of these attractions? b. What is the probability 35 called? c. Are the events mutually exclusive? Explain.

a) 55%

b) Joint Probability

c) They are not mutually exclusive

Explanation:

Part 1 of the Question

First, we determine the formula for calculating the probabilities of Yellowstone Park and the Tetons as follows

Probability of Yellow Stone = p(Yellowstone)= 0.5 or 50%

Probability of Tetons = p(Tetons)= 0.4 or 40%

Probability of Both = p(Both)= 0.35 or 35%

Therefore, the probability of visiting at least one by a vacationer is as follows:

p(At least One) =  p(Yellowstone or Tetons)

=  p(Yellowstone) + p(Tetons) - p(Both)

= 50%+40%-35%

= 0.5+0.4-0.35

= 0.55 or 55%

Part 2 of the Question

First the probability of 35% represents the possibility of a vacationer visiting the two locations, hence, it can be called the percentage of intersection between Tetons and Yellowstone. It is also referred to as joint probability

Part 3 of the Question

Once event are mutually exclusive, it means they cannot be carried out or considered together. In other words, one becomes an alternate cost for the other. This means going to Yellowstone means the vacationer cannot go to Tetons and vice versa. In this situation, the joint probability will not be possible (0%). Since, we already know that there is a joint probability of 35%, it means the events are not mutually excusive