InterviewSolution
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InterviewSolution
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A box contains cards bearing numbers 6 to 70. If one card is frawn 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» Correct Answer - `(i) 4/65 (ii) 1/5 (iii) 12/65 (iv) 3/25` Given numbers 6,7,8,…,70 form an AP with a = 6 and d = 1. Let` T_(n) = 70." Then, " 6+(n-1) xx 1 = 64 rArr n = 65`. ` :. ` total numbers of cards = 65. (i) Out of the given numbers, the one-digit numbers are 6,7,8,9. Number of one-digit numbers = 4. ` :. ` P(getting a one-digit number) =` 4/65`. (ii) Out of the given numbers, those divisible by 5 are` 10,15,20,25,...,70`. Let ` T_(n) = 70.` Then, ` 10 + (n-1) xx 5 = 70 rArr (n-1) xx 5 = 60 rArr n -1 = 12 rArr n = 13`. ` :. ` p(getting a number divisible by 5) ` = 13/65 = 1/5`. (iii) Out of the given numbers, odd numbers less than 30 are 7,9,11,13,...,29. Let ` T_(n) = 29 `. Then, ` 7 +(m-1) xx 2 = 29 rArr (m-1) xx 2 = 22 rArr m -1 = 11 rArr m = 12`. ` :.` P(getting an odd number less than 30) = ` 12/65`. (iv) Number of numbers between 50 and 70 = numbers from 51 to 69. Their number = ` (69-51) + 1 = 19`. Prime number between 50 and 70 = 53, 59, 61, 67. Number of prime numbers = 4. Number of composite numbers = 19-4 = 15. ` :.` P(getting a composite numbers) ` = 15/65 = 3/13`. |
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