Short Note

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 an odd number less than 30.

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#### Solution

Let E_{3} be the event of getting an odd number less than 30.

Out of these numbers, odd numbers less than 30 are 7, 9, 11, ... , 29.

Given number 7, 9, 11, .... , 29 form an AP with a = 7 and d = 2.

Let T_{n} = 29. Then,

7 + (n − 1)2 = 29

⇒ 7 + 2n − 2 = 29

⇒ 2n = 24

⇒ n = 12

Thus, number of favourable outcomes = 12.

∴ P(getting an odd number less than 30) = P(E_{3}) = `("Number of outcomes favourable to" E_3)/"Number of all possible outcomes"`

Thus, the probability that the card bears an odd number less than 30 is `12/65`.

Concept: Concept Or Properties of Probability

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