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Three numbers are chosen from 1 to 30. The probability that they are not consecutive is

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Three numbers are chosen from 1 to 30. The probability that they are not consecutive is A. 142 145 B. 144 145 C. 143 145 D. 1 145 Select the correct answer from above options

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Correct Answer - B Out of 30 numbers from 1 to 30, three numbers can be chosen in .30C3 ways. So, total number of elementary events =.30C3 . Three consecutive numbers can be chosen in one of the following ways : (1,2,3),(2,3,4),..,(28,29,30) . ∴ Number of elementary events in which three numbers are consecutive is 28. Thus, Probability that the numbers are consecutive = 28 .30C3 = 1 145 Hence, required probability =1- 1 145 = 144 145

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