Question

A bag contain 5 blue balls and unknown numbers of x red balls. Two balls randomly drawn out.if the probability of both of them of being blue is 5/14.find x

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{red}\mathrm{balls}\mathrm{be}\mathrm{x} \\ \mathrm{number}\mathrm{of}\mathrm{blue}\mathrm{balls}=5 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{balls}=\mathrm{number}\mathrm{of}\mathrm{red}\mathrm{balls}+\mathrm{number}\mathrm{of}\mathrm{blue}\mathrm{balls} \\ =\mathrm{x}+5 \\ \mathrm{Probability}\mathrm{of}\mathrm{drawing}\mathrm{a}\mathrm{red}\mathrm{ball}=\frac{\mathrm{x}}{\mathrm{x}+5} \\ \mathrm{Probability}\mathrm{of}\mathrm{drawing}\mathrm{a}\mathrm{blue}\mathrm{ball}=\frac{5}{\mathrm{x}+5} \\ \mathrm{Also}\mathrm{Probability}\mathrm{of}\mathrm{drawing}\mathrm{a}\mathrm{blue}\mathrm{ball}=\frac{5}{14} \\ \Rightarrow \frac{5}{\mathrm{x}+5}=\frac{5}{14} \\ \Rightarrow 70=5\mathrm{x}+25 \\ \Rightarrow 45=5\mathrm{x} \\ \Rightarrow \mathrm{x}=9 \end{gathered}$$
Regards