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प्रश्न
Cards marked with numbers 1, 3, 5, ..., 101 are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number less than 20.
उत्तर
Given number 1, 3, 5, ..., 101 form an AP with a = 1 and d = 2.
Let Tn = 101. Then,
1 + (n − 1)2 = 101
⇒ 1 + 2n − 2 = 101
⇒ 2n = 102
⇒ n = 51
Thus, total number of outcomes = 51.
Let E2 be the event of getting a prime number less than 20.
Out of these numbers, prime numbers less than 20 are 3, 5, 7, 11, 13, 17 and 19.
Thus, number of favourable outcomes = 7.
∴ P(getting a prime number less than 20) = P(E2) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`
`= 7/51`
Thus, the probability that the number on the drawn card is a prime number less than 20 is `7/51`.
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