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

Answer 1

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) = \[\frac{n\left( E_1 \right)}{n\left( S \right)} = \frac{^{8}{}{C}_2}{^{20}{}{C}_2} = \frac{14}{95}\]