Question

The odds against A solving the problem are 4 to 3 and the odds in favour of B solving the problem are 7 to 5. Find the probability that the problem will be solved.

Answer 1

Probability of A does not solve the problem = $\frac{4}{7}$ ...A

Probability of A solves the problem = $\frac{3}{7}$ ...A

Probability of B does not solve the problem = $\frac{5}{12}$

Probability of B solves the problem $=\frac{7}{12}$

Probability that the problem get solved $=\frac{4}{7}\times \frac{7}{12}+\frac{3}{7}\times \frac{5}{12}+\frac{3}{7}\times \frac{7}{12}$

$=\frac{64}{84}=\frac{16}{21}$