$1500$ 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 girl
Also,check whether the sum of these probabilities is $1$.
| 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 girl
Also,check whether the sum of these probabilities is $1$.
(N/A) Total number of families $= 475 + 814 + 211 = 1500$.
$(i)$ Number of families having $2$ girls $= 475$.
Probability $(P_1)$ of a randomly chosen family having $2$ girls $= \frac{475}{1500} = \frac{19}{60}$.
$(ii)$ Number of families having $1$ girl $= 814$.
Probability $(P_2)$ of a randomly chosen family having $1$ girl $= \frac{814}{1500} = \frac{407}{750}$.
$(iii)$ Number of families having no girl $= 211$.
Probability $(P_3)$ of a randomly chosen family having no girl $= \frac{211}{1500}$.
Sum of all these probabilities $= P_1 + P_2 + P_3 = \frac{475}{1500} + \frac{814}{1500} + \frac{211}{1500} = \frac{475 + 814 + 211}{1500} = \frac{1500}{1500} = 1$.
Therefore,the sum of all these probabilities is $1$.
$(i)$ Number of families having $2$ girls $= 475$.
Probability $(P_1)$ of a randomly chosen family having $2$ girls $= \frac{475}{1500} = \frac{19}{60}$.
$(ii)$ Number of families having $1$ girl $= 814$.
Probability $(P_2)$ of a randomly chosen family having $1$ girl $= \frac{814}{1500} = \frac{407}{750}$.
$(iii)$ Number of families having no girl $= 211$.
Probability $(P_3)$ of a randomly chosen family having no girl $= \frac{211}{1500}$.
Sum of all these probabilities $= P_1 + P_2 + P_3 = \frac{475}{1500} + \frac{814}{1500} + \frac{211}{1500} = \frac{475 + 814 + 211}{1500} = \frac{1500}{1500} = 1$.
Therefore,the sum of all these probabilities is $1$.
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