Chapter 5.2, Problem 56E

To determine

To compute: The probability that a chosen student eats fish or eggs.

Answer to Problem 56E

The correct option is b. $\frac{13}{20}$

Explanation of Solution

Given information:

Total number of students $=\text{ 275}$

Number of vegetarians $=\text{ 2}0$

Number of vegetarians who eat both fish and egg $=\text{ 9}$

Number of vegetarians who eat egg but not fish $=\text{ 3}$

Number of vegetarians who don’t eat any of them $=\text{ 7}$

Formula used:

  $\begin{array}{l}\text{Number of student who eat fish or eat }=\text{ Number ofstudents who eat fish }+\\ \text{ Number of students who eat egg }–\text{ Number of students whoeat both fish and egg}.\end{array}$

  $\text{P (a chosen student eats fish or egg) = }\frac{\text{Number of vegetarians who eat fish or egg}}{\text{Total number of vegetarians}}$

Calculation:

Let x be the number of vegetarians who eat fish but not egg.

So, $\text{2}0=\text{ x }+\text{ 9 }+\text{ 3 }+\text{ 7}$

  $\text{x }=\text{ 1}$

Illustrating the data in Venn diagram

  

Number of students who eat fish or eat $=\text{ 1}0+\text{ 12 }–\text{ 9 }=\text{ 13}$

P (a chosen student eats fish or egg) $=\frac{13}{20}$ .