Question

In a sample of$275$students, $20$say they are vegetarians. Of the vegetarians, $9$eat both fish and eggs, $3$eat eggs but not fish, and $7$eat neither. Choose one of the vegetarians at

random. What is the probability that the chosen student eats fish or eggs?

a. $9/20$

b. $13/20$

c. $22/20$

d. $9/275$

e.$22/275$

Short answer

The probability that the student chooses a fish or egg is (b)$\frac{13}{20}$.

Step-by-step solution

Given Information

We are given the values of a total vegetarian and a vegetarian who eats both fish and eggs, and another who eats eggs but not fish, and another who doesn't eat both, and we have to find out the probability that the student eats fish or eggs.

Explanation

According to the question, from$275$students$20$are vegetarians, and from the vegetarian$9$eat both fish and eggs, data-custom-editor="chemistry" $3$eat eggs but not fish, and $7$eat neither.

First, find out the probability of eating fish but not eggs, that is,

probability of eating fish but not eggs=$20-9-3-7$,

On solving, we get$P(Fishbutnoteggs)=1$

$P(Eatfishoreggs)=\frac{favourableoutcomes}{totaloutcomes}$

favorable outcomes is $9+3+1=13$and total outcomes is$20$.

Put these values,

P(Eat fish or eggs)$=\frac{13}{20}$.

Hence, the probability of eating fish or egg is$\frac{13}{20}$.