Question

The odds in favour of A solving a problem are 3 to 4 and the odds against B solving the same problem are 5 to 7. If they both try the problem, the probability that the problem is solved is
1. \(\frac{{41}}{{84}}\)
2. \(\frac{{16}}{{21}}\)
3. \(\frac{5}{{21}}\)
4. \(\frac{1}{4}\)

Answer 1

Correct Answer - Option 2 : \(\frac{{16}}{{21}}\)

Given:

The odds in favour of A solving a problem are 3 to 4

The odds against B solving the same problem are 5 to 7

Formula used:

Probability = Favourable outcomes/Total number of outcomes

Calculation:

Probability of solving the problem by A = 3/7

Probability of not solving the problem by A = 1 – 3/4 = 4/7

Probability of not solving the problem by B = 5/12

The probability that the problem is solved = 1 – None of them solves the problem

⇒ 1 – (4/7) × (5/12)

⇒ 1 – 5/21 

⇒ 16/21

∴ The probability of solving the problem is 16/21