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Question
n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.
Solution
It is given that n (≥ 3) persons are seated in a row and two persons are selected.
∴ Total number of elementary event = n(S) = nC2
Let E be the event associated with the experiment that two persons are together.
∴ n(E) = n -1C1
Thus, required probability = P(E) = \[\frac{n(E)}{n(S)}\]
= \[\frac{^{n - 1}{}{C}_1}{^{n}{}{C}_2}\]
= \[\frac{\left( n - 1 \right)}{\frac{n\left( n - 1 \right)}{2}} = \frac{2\left( n - 1 \right)}{n\left( n - 1 \right)} = \frac{2}{n}\]
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