Question

Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a prime number less than 15,

Answer 1

Given number 1, 3, 5, .... , 35 form an AP with a = 1 and d = 2.
Let T_n = 35. Then,
1 + (n − 1)2 = 35
⇒ 1 + 2n  − 2 = 35
⇒ 2n = 36
⇒ n = 18

Thus, total number of outcomes = 18.

 Let E₁ be the event of getting a prime number less than 15.

Out of these numbers, prime numbers less than 15 are 3, 5, 7, 11 and 13.

Number of favourable outcomes = 5.

∴ P(getting a prime number less than 15) = P(E₁) = `("Number of outcomes favourable to" E_1)/"Number of all possible outcomes"`

`=5/18`

Thus, the probability of getting a card bearing a prime number less than 15 is  `5/18`.