Question

The odds against A solving a certain problem are 3 to 2 and the odds in favour of B solving the same problem are 2 to 1 . The probability that the problem will be solved if they both try, is

• A. $\frac{2}{5}$
• B. $\frac{11}{15}$
• C. $\frac{4}{5}$
• D. $\frac{2}{3}$

Answer 1

Answer: (C)

Probability of A solving the problem $=\frac{2}{5}$.
Probability of B solving the problem $=\frac{2}{3}$
As A's solving the problem and B's solving the problem are two independent events, required probability $=\frac{2}{5}+\frac{2}{3}-\frac{2}{5} \times \frac{2}{3}=\frac{4}{5}$