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Q.

State true or false.

In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is $14$ .

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a

True

b

False

answer is B.

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Detailed Solution

We need to check the validification of the statement, in a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is

14

.

P (E) = n (E) n (S)

Considering that in a family there will be three children, there may be no girl, one girl, two girls or three girls.
Let us consider boy to be b and girl to be g.
The possible outcomes are

{B B B, B B G, B G B, B G G, G B B, G B G, G G B, G G G}

There is a total of

8

possible outcomes.
The probability of having

0

girls

= 18

The probability of having

1

girl

= 38

The probability of having

2

girls

= 38

The probability of having

3

girls

= 18

The probability of having no girl, one girl, two girls or three girls is

\frac{1}{8} + \frac{3}{8} + \frac{3}{8} + \frac{1}{8} = \frac{6}{8} = \frac{3}{4}

.
The probability of each case is different and not equal to

14

.
The probability of having no girl, one girl, two girls or three girls is

\frac{3}{4}

.
So, the given statement is false.
Hence, the statement is false and the correct option is 2.

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