Question

A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that  on one there is a prime number and on the other there is a multiple of 4.as

Answer 1

Clearly, the sample space is given by S = {1, 2, 3, 4, 5,...19, 20}. 
∴ n(S) = ²⁰C₂ = 190

Let E₂ be the event where one ticket has a prime number, while the other has a multiple of 4.
Then prime numbers = {2, 3, 5, 7, 11, 13, 17, 19}
and multiples of 4 = {4, 8, 12, 16, 20}
∴ Favourable number of ways, n(E₂) = ⁸C₁× ⁵C₁ = 8 × 5 = 40
Hence, required probability, P(E₂ ) = \[\frac{n\left( E_2 \right)}{n\left( S \right)} = \frac{40}{190} = \frac{4}{19}\]