Question

A box contains cards bearing numbers 6 to 70. If one card is drawn at random from the box, find the probability that it bears a one-digit number.

Answer 1

Given number 6, 7, 8, ...., 70 form an AP with a = 6 and d = 1.

Let T_n = 70. Then,

6 + (n − 1)1 = 70

⇒ 6 + n  − 1 = 70

⇒ n = 65

Thus, total number of outcomes = 65.

Let E₁ be the event of getting a one-digit number.

Out of these numbers, one-digit numbers are 6, 7, 8 and 9.

Number of favourable outcomes = 4.

∴ P(getting a one-digit number) = P(E₁) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`

`= 4/65`

Thus, the probability that the card bears a one-digit number is `4/65`.