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प्रश्न
Cards bearing numbers 1, 3, 5, .... , 35 are kept in a bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a prime number less than 15,
उत्तर
Given number 1, 3, 5, .... , 35 form an AP with a = 1 and d = 2.
Let Tn = 35. Then,
1 + (n − 1)2 = 35
⇒ 1 + 2n − 2 = 35
⇒ 2n = 36
⇒ n = 18
Thus, total number of outcomes = 18.
Let E1 be the event of getting a prime number less than 15.
Out of these numbers, prime numbers less than 15 are 3, 5, 7, 11 and 13.
Number of favourable outcomes = 5.
∴ P(getting a prime number less than 15) = P(E1) = `("Number of outcomes favourable to" E_1)/"Number of all possible outcomes"`
`=5/18`
Thus, the probability of getting a card bearing a prime number less than 15 is `5/18`.
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