Question

1400 families with 3 children were surveyed and it was found that 200 families has 0 girls, 812 families has 1 girl , 210 families has 2 girls and 178 families has 3 girls
If a family is chosen at random compute the probability that it has
1. 1girl
2. 1 boy

Answer 1

$$\begin{gathered} \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{families}=1400 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}=1400 \\ \left(1\right). \\ \mathrm{Number}\mathrm{of}\mathrm{families}\mathrm{having}1\mathrm{girl}=812 \\ \mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}=812 \\ \mathrm{Required}\mathrm{probability}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{no}.\mathrm{of}\mathrm{possible}\mathrm{outcomes}}=\frac{812}{1400}=0.58 \\ \left(2\right). \\ \mathrm{Number}\mathrm{of}\mathrm{families}\mathrm{with}1\mathrm{boy}\mathrm{or}\mathrm{having}2\mathrm{girls}=210 \\ \mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}=210 \\ \mathrm{Required}\mathrm{probability}=\frac{\mathrm{no}.\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{total}\mathrm{no}.\mathrm{of}\mathrm{possible}\mathrm{outcomes}}=\frac{210}{1400}=0.15 \end{gathered}$$