$1500$ families with $2$ children were selected randomly, and the following data were recorded:

Number of girls in a family	$2$	$1$	$0$
Number of families	$475$	$814$	$211$

Compute the probability of a family, chosen at random, having$( i)\ 2$ girls $( ii)\ 1$ girl $( iii)$ No girlAlso check whether the sum of these probabilities is $1$.

Given: $1500$ families with $2$ children were selected randomly, and the following data were recorded:

To do: To compute the probability of a family, chosen at random, having

$( i)\ 2$ girls        $( ii)\ 1$ girl       $( iii)$ No girl

Also check whether the sum of these probabilities is $1$.

Solution:

$( i)$. Total number of families$=475+814+211=1500$

Number of families having $2$ girls$=475$

Probability of having $2$ girls$=\frac{Number\ of\ families\ having\ 2\ girls}{Total\ number\ of\ families}$

$=\frac{475}{1500}$

$=\frac{19}{60}$

$( ii)$. Here, total number of families$=475+814+211=1500$

Number of families having $1$ girl$=814$

Probability of having $1$ girl$=\frac{Number\ of\ families\ having\ 1\ girl}{Total\ number\ of\ families}$

$=\frac{814}{1500}$

$=\frac{407}{750}$

$( iii)$. Here, total number of families$=1500$

Number of families having no girl$=211$

Probability of having $1$ girl$=\frac{Number\ of\ families\ having\ no\ girl}{Total\ number\ of\ families}$

$=\frac{211}{1500}$

$=\frac{211}{1500}$

Sum of all these probabilities$=\frac{19}{60}+\frac{407}{750}+\frac{211}{750}$

$=\frac{475}{1500}+\frac{814}{1500}+\frac{211}{1500}$

$=\frac{475+814+211}{1500}$

$=\frac{1500}{1500}$

$=1$

Thus, the sum of all these probabilities is $1$.

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Updated on: 10-Oct-2022

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