Question

In a group of school children 3 individual qualities ( honesty, kindness, patience)are found. The probability of selecting a honest child and probability of selecting a kind child are 4/15 And 2/5 respectively. All of them are likely to be selected. If the number of patient child is 10 what is the total number of children in that group?

Answer 1

Dear Student,


$$\begin{gathered} \mathrm{Since}\mathrm{all}\mathrm{the}\mathrm{student}\mathrm{are}\mathrm{likely}\mathrm{to}\mathrm{be}\mathrm{selected}\mathrm{in}\mathrm{any}\mathrm{of}\mathrm{the}3\mathrm{category}. \\ \mathrm{Probability}\mathrm{of}\mathrm{all}\mathrm{included}\mathrm{will}\mathrm{be}1 \\ \frac{4}{15}+\frac{2}{5}+\mathrm{x}=1 \\ \Rightarrow \mathrm{x}=\frac{1}{3}\left(\mathrm{probability}\mathrm{of}\mathrm{selecting}\mathrm{patient}\mathrm{child}\right) \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{patient}\mathrm{children}\mathrm{is}10. \\ \mathrm{x}=\frac{\mathrm{Number}\mathrm{of}\mathrm{patient}\mathrm{children}}{\mathrm{total}\mathrm{no}.\mathrm{of}\mathrm{children}} \\ \Rightarrow \frac{1}{3}=\frac{10}{\mathrm{total}\mathrm{no}.\mathrm{of}\mathrm{children}} \\ \Rightarrow \mathrm{total}\mathrm{no}.\mathrm{of}\mathrm{children}=30 \end{gathered}$$
Regards.