The odds against A solving a problem are 8 to 6 and the odds in favour of B solving the same problem are 14 to 10. The probability of solving the problem if they both try independently is

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$\frac{16}{21}$

$\frac{5}{21}$

$\frac{4}{21}$

$\frac{1}{3}$

answer is A.

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Detailed Solution

$\begin{array}{rcl} P (A) : P (A) & = & 8 : 6 \Rightarrow P (A) = \frac{6}{14} \\ P (B) : P (B) & = & 14 : 10 \Rightarrow P (B) = \frac{14}{24} \\ P (A \cup B) & = & P (A) + P (B) - P (A) \cdot P (B) \\ = & \frac{6}{14} + \frac{14}{24} - \frac{6}{14} \cdot \frac{14}{24} = \frac{16}{21} \end{array}$

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