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Two buses A and B are scheduled to ·arrive at a town central bus station at noon. The probability that bus A will be late, is 1 /5. The probability that bus B will be late, is 7 /25. The probability that the bus B is late given that bus A is late, is 9/10, then the probability bus A is late given that bus B is late, is

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$\frac{12}{18}$

$\frac{7}{10}$

$\frac{18}{28}$

$\frac{2}{28}$

answer is C.

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Detailed Solution

Given, $\begin{array}{rr} P (A) = \frac{1}{5}, P (B) = \frac{7}{25} \\ P (B / A) = \frac{9}{10} \end{array}$

To find P(A I B)

Now, $P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)} = \frac{P (A) P (\frac{B}{A})}{P (B)}$

$= \frac{\frac{1}{5} \times \frac{9}{10}}{\frac{7}{25}} = \frac{9}{50} \times \frac{25}{7} = \frac{9}{14} = \frac{18}{28}$

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