Mathematics - Probability Question with Solution | TestHub

$P(A)=\frac{2}{5}$ For independent events, $$\begin{array}{rl}& P(A\cap B)=P(A)P(B)\Rightarrow P(A\cap B)\le \frac{2}{5}\\ & \Rightarrow P(A\cap B)=\frac{1}{10},\frac{2}{10},\frac{3}{10},\frac{4}{10}\\ & \text{ (i) }P(A\cap B)=\frac{1}{10}\\ & \Rightarrow P(A)\cdot P(B)=\frac{1}{10}\\ & \Rightarrow P(B)=\frac{1}{10}\times \frac{5}{2}=\frac{1}{4},\text{ not possible. }\\ & \text{ (ii) }P(A\cap B)=\frac{2}{10}\Rightarrow \frac{2}{5}\times P(B)=\frac{2}{10}\\ & \Rightarrow P(B)=\frac{5}{10},\text{ outcomes of }B=5\end{array}$$ $$\text{ (iii) }\begin{array}{rl}& P(A\cap B)=\frac{3}{10}\Rightarrow P(A)\cdot P(B)=\frac{3}{10}\\ & \Rightarrow \frac{2}{5}\times P(B)=\frac{3}{10}\\ & P(B)=\frac{3}{4},\text{ not possible }\end{array}$$ $$\text{ (iv) }\begin{array}{rl}& P(A\cap B)=\frac{4}{10}\\ \Rightarrow & P(A)\cdot P(B)=\frac{4}{10}\\ \Rightarrow & P(B)=1,\text{ outcomes of }B=10.\end{array}$$