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Question
The probabilities of two students A and B coming to the school in time are \[\frac{3}{7}\text { and }\frac{5}{7}\] respectively. Assuming that the events, 'A coming in time' and 'B coming in time' are independent, find the probability of only one of them coming to the school in time. Write at least one advantage of coming to school in time.
Solution
\[P\left( \text{ A coming in time } \right) = \frac{3}{7}\]
\[P\left( \text{ A not coming in time } \right) = 1 - \frac{3}{7} = \frac{4}{7}\]
\[P\left( \text{ B coming in time } \right) = \frac{5}{7}\]
\[P\left( \text{ B not coming in time } \right) = 1 - \frac{5}{7} = \frac{2}{7}\]
\[P\left( \text{ only one of A and B coming in time } \right) = P\left( A \right) P\left( \bar{B} \right) + P\left( \bar{A} \right)P\left( B \right)\]
\[ = \frac{3}{7} \times \frac{2}{7} + \frac{4}{7} \times \frac{5}{7}\]
\[ = \frac{6}{49} + \frac{20}{49}\]
\[ = \frac{26}{49}\]
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