The probabilities of two students A and B coming to the school in time are $\frac{3}{7}$ 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.

This question appeared in 65-1,65-2 and 65-3 versions of the paper in 2013.

Let $P(A)=\large \frac{3}{7}$ (ie) Probability of A coming in time.
Therefore $P(A^1)=1-\large \frac{3}{7}$$=\large \frac{4}{7}(ie) Probability of A not coming in time. P(B)=\large \frac{5}{7} (ie) Probability of B coming in time. P(B^1)=1-\large \frac{5}{7}$$=\large \frac{2}{7}$(ie) Probability of B not coming in time.
Therefore Probability of only one of them coming to school in time is
$P(A).P(B^1)+P(B)+P(A^1)$
$=\large \frac{3}{7}.\frac{2}{7}+\frac{5}{7}.\frac{4}{7}$
$=\large \frac{6}{49}+\frac{20}{49}=\frac{26}{49}$
Hence the probability of only one of them coming to school in time is $\large \frac{26}{49}$
The advantage of coming to school in time is we can relax ourselves and concentrate more during the class.

edited Jul 8, 2013