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 t…

Question

asked Jan 3, 2022 108k views

1 Answer

Nelson Orland · Answer 1 · 2022-01-09T22:41:05+0000

Answer:

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.