Question

The odds against A solving a certain problem are $4$ to $3$ and the odds in favour of B solving the same problem are $7$ to $5$. If both of them try independently, the probability that the problem will be solved is :

• A. $\frac{11}{21}$
• B. $\frac{13}{21}$
• C. $\frac{16}{21}$
• D. $\frac{8}{21}$

Answer 1

The correct option is C $\frac{16}{21}$

Probability that A solves the problem, $P\left(A\right)=1-\frac{4}{7}=\frac{3}{7}$

Probability that B solves the problem, $P\left(A\right)=1-\frac{5}{12}=\frac{7}{12}$

The required probability $=P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$

$=\frac{3}{7}+\frac{7}{12}-\frac{3}{7}\times \frac{7}{12}$ $\because P(A\cap B)=P\left(A\right)\times P\left(B\right)$

$=\frac{85}{84}-\frac{21}{84}$

$=\frac{16}{21}$