Mathematics - Probability Question with Solution | TestHub

Let $A$ be the event that maximum is $6$. $B$ be event that minimum is $3$ $P(A)=\frac{{}^5{C}_2}{{}^8{C}_3}$ (the numbers $<6$ are $5$) $P(B)=\frac{{}^5{C}_2}{{}^8{C}_3}$ (the numbers $>3$ are $5$) $P(A\cap B)=\frac{{}^2{C}_1}{{}^8{C}_3}$ Required probability is $\mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right)=\frac{\mathrm{P}(\mathrm{A}\cap \mathrm{B})}{\mathrm{P}(\mathrm{A})}=\frac{{}^2{\mathrm{C}}_1}{{}^5{\mathrm{C}}_2}=\frac{2}{10}=\frac{1}{5}$.