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?

Answer 1

We know that there is sample of 275 MHS Students

20 are vegetarians

       9 eat both fish and eggs

       3 eat eggs but not fish

       8 eat neither

Total 20

 

In a table:

            FISH FISHc TOTAL

EGGS     9        3       12

EGGSc   1         7        8

TOTAL    10       10      20

 

P(F U E) = 9 + 3 + 1 / 20 = 13/20 = 0.65

Or

P(F U E) = 10/20 + 12/20 -9/20 = 13/20 = 0.65

Answer 2

The probability that the chosen student eats fish or eggs is $\dfrac{13}{20}$.

According to the questions, 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.

So,

20 are vegetarians.

Number of students who eat fish but not eggs is $20-9-7-3=1$.

Now, probability that the chosen student eats fish or eggs is-

$P=\dfrac{favourable\;number\;of\;outcomes}{total\;number\;of\;outcomes}\\P=\dfrac{eats\;fish\;or\;eggs}{20}\\P=\dfrac{9+3+1}{20}\\P=\dfrac{eats\;fish\;only+eats\;eggs\;only+eats\;both}{20}\\P=\dfrac{13}{20}$

Hence, the probability that the chosen student eats fish or eggs is $\dfrac{13}{20}$.

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