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Question
A box contains cards numbered 3, 5, 7, 9, .... , 35, 37. A card is drawn at random from the box. Find the probability that the number on the card is a prime number.
Solution
Given numbers 3, 5, 7, 9, .... , 35, 37 form an AP with a = 3 and d = 2.
Let Tn = 37. Then,
3 + (n − 1)2 = 37
⇒ 3 + 2n − 2 = 37
⇒ 2n = 36
⇒ n = 18
Thus, total number of outcomes = 18.
Let E be the event of getting a prime number.
Out of these numbers, the prime numbers are 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 and 37.
Number of favourable outcomes = 11.
∴ P(getting a prime number) = P(E) = `("Number of outcomes favourable to" E )/"Number of all possible outcomes"`
Thus, the probability that the number on the card is a prime number is `11/18`.
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