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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 an odd number less than 30.
Solution
Let E3 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 Tn = 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(E3) = `("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`.
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