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Question
A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that both the tickets have prime numbers on them
Solution
Clearly, the sample space is given by S = {1, 2, 3, 4, 5,...19, 20}.
∴ n(S) = 20C2 = 190
Let E1 be the event where both the tickets have prime numbers on them.
Then E1 = {2, 3, 5, 7, 11, 13, 17, 19}
∴ Favourable number of ways = n(E1) = 8C2
Hence, required probability = P(E1) = \[\frac{n\left( E_1 \right)}{n\left( S \right)} = \frac{^{8}{}{C}_2}{^{20}{}{C}_2} = \frac{14}{95}\]
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