Question

The odds against A solving a problem are $8$ to $6$ and the odds in favour of B solving the same problem $14$ to $12$. The probability of solving the problem if they both try independently is

• A. $\frac{67}{91}$
• B. $\frac{5}{21}$
• C. $\frac{4}{21}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{67}{91}$

$P\left(A\right)=$ Probability of $A$ solving the problem $=\frac{6}{8+6}=\frac{3}{7}$

$P\left(B\right)=$ Probability of $B$ solving the problem $=\frac{14}{14+12}=\frac{7}{13}$

$\therefore$ $P(A\cup B)=$ Probability of $A$ & $B$ solving the problem independently

$=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=P\left(A\right)+P\left(B\right)-P\left(A\right).P\left(B\right)$ $(\because$ if $A$ and $B$ are independent)

$=\frac{3}{7}+\frac{7}{13}-\frac{3}{13}$ events then $P(A\cap B)=P\left(A\right).P\left(B\right)$ $)$

$=\frac{39+49-21}{91}$

$=\frac{88-21}{91}$

$=\frac{67}{91}$ (Ans.)