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

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) (2/5) (B) (11/15) (C) (4/5) (D) (2/3)

Tardigrade Admin · Accepted Answer

Probability of A solving the problem =(2/5). Probability of B solving the problem =(2/3) As A's solving the problem and B's solving the problem are two independent events, required probability =(2/5)+(2/3)-(2/5) × (2/3)=(4/5)

Q. 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

$\frac{2}{5}$

$\frac{11}{15}$

$\frac{4}{5}$

$\frac{2}{3}$

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 $= \frac{2}{5} + \frac{2}{3} - \frac{2}{5} \times \frac{2}{3} = \frac{4}{5}$