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

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:

Options:

A . 4184

B . 1621

C . 521

D . 14

Answer: Option B
:
B

P (A) = \frac{3}{7}, P (B) = \frac{7}{12} P (¯ A) = \frac{4}{7}, P (¯ B) = \frac{5}{12} P (A \cup B) = 1 - P (¯ ¯¯¯¯¯¯¯¯¯¯¯¯ ¯ A \cup B) = 1 - P (¯ A \cap ¯ B) ∴ P (A \cup B) = 1 - \frac{4}{7} \times \frac{5}{12} = \frac{16}{21}

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