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InterviewSolution
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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(i) a one-digit number,(ii) a number divisible by 5,(iii) an odd number less than 30,(iv) a composite number between 50 and 70. |
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Answer» Apply general term formula of an AP, to find the total numbers of cards. Here a (first term) = 6, d (common difference) = 1 and l( last term) = 70 l = a + (n-1)d 70 = 6 + (n-1)(1) n = 65 Total number of cards = 65 (i) Favorable outcome = a one-digit number = 6, 7, 8, 9 Favorable number of outcomes = 4 P(getting a one-digit number) = 4/65 (ii) Favorable outcome = a number divisible by 5 = 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70 Favorable number of outcomes = 13 P(getting a number divisible by 5) = 13/65 = 1/5 (iii) Favorable outcome = an odd number less than 30 = 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29 Favorable number of outcomes = 12 P (getting a odd number less than 30) = 12/65 (iv) Favorable outcome = a composite number between 50 and 70 = 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69 The number of favorable outcomes = 15 P(getting a composite number between 50 and 70) = 15/65 = 3/13 |
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