Question

n (≥ 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

 

Answer 1

 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 -1C_¹ 
Thus, required probability = P(E) = \[\frac{n(E)}{n(S)}\]

                                         = \[\frac{^{n - 1}{}{C}_1}{^{n}{}{C}_2}\]

                                         = \[\frac{\left( n - 1 \right)}{\frac{n\left( n - 1 \right)}{2}} = \frac{2\left( n - 1 \right)}{n\left( n - 1 \right)} = \frac{2}{n}\]