Question

Of 60 diners in a restaurant, 15 ordered the fish of the day and 7 are wearing a tie. Of the diners who ordered fish, 2 are wearing a tie. Which is the probability that one of the diners ordered the fish or is wearing a tie?

A. 0.37
B. 0.03
C. 0.5
D. 0.33

Answer 1

D. 0.33

Explanation:

To solve this question, we use Venn probabilities.

I am going to say that:

Event A: Ordered fish of the day.

Event B: Are wearing a tie.

Of 60 diners in a restaurant, 15 ordered the fish of the day

This means that
`P(A) = (15)/(60)`

7 are wearing a tie.

This means that
`P(B) = (7)/(60)`

Of the diners who ordered fish, 2 are wearing a tie.

This means that
`P(A \cap B) = (2)/(60)`

Which is the probability that one of the diners ordered the fish or is wearing a tie?

This is:

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

Replacing with the values we have:

`P(A \cup B) = (15)/(60) + (7)/(60) - (2)/(60) = (15 + 7 - 2)/(60) = (20)/(60) = 0.33`

The correct answer is given by option d.