$1500$ 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:
Number of girls | $2$ | $1$ | $0$ |
Number of families | $475$ | $814$ | $211$ |
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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