Question

Twenty of a sample of $275$ students say they are vegetarians. Of the vegetarians, $9$eat both fish and eggs, $3$ eat eggs but not fish, and $8$ eat neither. Choose one of the vegetarians at random. What is the probability

that the chosen student eats neither fish nor eggs?

(a) $8/275=0.03$ (c) $8/20=0.4$ (e) $1$

(b) $20/275=0.07$ (d)

Short answer

The correct option is (c) $8/20=0.4$

Step-by-step solution

Step 1. Given Information

There are $275$ pupils in total. There are $20$ vegetarian students in the class.

A total of $9$ vegetarian students eat both fish and eggs. A total of $3$ vegetarian students consume eggs but not fish. There are $7$ vegetarian students who eat neither.

Step 2. Concept Used

Formula's used$Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Step 3. Calculation

Total sample space = $20$

Both fish and eggs should be consumed$P(A\cup B)=9$

$P(studentseatsneitherfishnoreggs)=\frac{nooffavorableoutcomes}{numberofpossibleoutcomes}$

$P(studentseatsneitherfishnoreggs)=8/20$

$P(studentseatsneitherfishnoreggs)=0.4$

The probability that chosen $P(studentseatsneitherfishnoreggs)=0.4$