Question

A person has $3$ shares in a lottery containing $2$ prizes and $8$ blanks. The chance of getting prize is

• A. $\frac{12}{28}$
• B. $\frac{3}{8}$
• C. $\frac{7}{15}$
• D. $\frac{8}{15}$

Answer 1

The correct option is A $\frac{12}{28}$

$WLL,WWL,WWW$

$WLL{=}^3{C}_1{\times }^9{C}_2$
$WWL{=}^3{C}_2{\ast }^9{C}_1$
$WWW{=}^3{C}^3{\times }^9{C}_0$
No of ways to chose $3$ tickes out of $12{=}^{1}2C_3$
$P\left(A\right)={(}^3{C}_1{\times }^9{C}_2{+}^3{C}_2{\times }^9{C}_1{+}^3{C}_3{\times }^9{C}_0){/}^{1}2C_0=34/55$

$P\left(B\right)={(}^2{C}_2{\times }^6{C}_0{+}^2{C}_1{\times }^6{C}_1)/8C2=\frac{12}{28}$

Hence,

option $\left(A\right)$ is correct answer.