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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 less than 19.
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 E1 be the event of getting a number less than 19.
Out of these numbers, numbers less than 19 are 1, 3, 5, ... , 17.
Given number 1, 3, 5, .... , 17 form an AP with a = 1 and d = 2.
Let Tn = 17. Then,
1 + (n − 1)2 = 17
⇒ 1 + 2n − 2 = 17
⇒ 2n = 18
⇒ n = 9
Thus, number of favourable outcomes = 9.
∴ P(getting a number less than 19) = P(E1) = `("Number of outcomes favourable to" E_2)/"Number of all possible outcomes"`
Thus, the probability that the number on the drawn card is less than 19 is `3/17`.
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