Question

A travel agency books holiday tours to Italy, Greece, and other countries in Europe. A supervisor notes that the probability that 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

Answer 1

Add them together. 0.94

Answer 2

72% of chances that a client chooses Greece, or Italy, or both.

Explanation:

First we have to the define the different types of probabilities.

When we need to find the probability of A and B, we have to multiply them:

`P(A) * P(B)` if they are independent.

`P(A) * P(B|A)` if they are dependent, that is, the probability of one event affects the other.

The probability of A or B, we have to sum:

`P(A) + P(B)` if they are mutually exclusive.

`P(A) + P(B) - P(A and B)` if they are not mutually exclusive.

Remember that mutually exclusive events can happen at the same time, like this problem, if a person visits Greece is because he exclude Italy, both events cannot happen at the same time. However, the problem is considering the whole tour, this changes the type of the events, making them not mutually exclusive, because in the same tour, the person can travel Greece and Italy, or vice versa.

In addition, both events are independent, because they outcome of one place doesn't change the probability of the other place. Therefore, the probability that is being ask is:

`P(A) + P(B) - P(A and B)`

Where
`P(A)=P(Greece)=0.28` and
`P(B)=P(Italy)=0.11, P(Greece and Italy)=0.11`

`P(Greece) + P(Italy) - P(Greece and Italy)`

`0.28 + 0.55 - 0.11= 0.72`

Therefore, the probability is 72%.