Question

Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number less than 20.

Answer 1

​Given number 1, 3, 5, ..., 101 form an AP with a = 1 and d = 2.

Let T_n = 101. Then,

1 + (n − 1)2 = 101

⇒ 1 + 2n  − 2 = 101

⇒ 2n = 102

⇒ n = 51

Thus, total number of outcomes = 51.

Let E₂ be the event of getting a prime number less than 20.

Out of these numbers, prime numbers less than 20 are 3, 5, 7, 11, 13, 17 and 19.

Thus, number of favourable outcomes = 7.

∴ P(getting a prime number less than 20) = P(E₂) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`

`= 7/51`

Thus, the probability that the number on the drawn card is a prime number less than 20 is `7/51`.