Question

It was found that 61 percent of the tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing. 33 percent visited Xi'an with its magnificent terracotta soldiers, horses, and chariots, which lay buried for over 2000 years. 18 percent of the tourists went to both Beijing and Xi'an. What is the probability that a tourist visited at least one of these places

Answer 1

0.76 = 76% probability that a tourist visited at least one of these places

Explanation:

I am going to solve this question using the probabilities as Venn sets.

We have that:

Event A: Tourist visited Beinjing.

Event B: Tourist visited Xi'an.

61 percent of the tourists to China visited the Forbidden City, the Temple of Heaven, the Great Wall, and other historical sites in or near Beijing.

This means that
`P(A) = 0.61`

33 percent visited Xi'an with its magnificent terracotta soldiers, horses, and chariots, which lay buried for over 2000 years.

This means that
`P(B) = 0.33`

18 percent of the tourists went to both Beijing and Xi'an.

This means that
`P(A \cap B) = 0.18`

What is the probability that a tourist visited at least one of these places?

This is

`P(A \cup B) = P(A) + P(B) - P(A \cap B)`

We already found these values. So

`P(A \cup B) = 0.61 + 0.33 - 0.18 = 0.76`

0.76 = 76% probability that a tourist visited at least one of these places