Question

Three numbers are chosen at random from 1 to 15. The probability that no two numbers are consecutive,

Answer 1

Probability = 3/15.

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Answer 2

Three numbers are chosen at random from 1 to 15. The Probability that all three numbers are consecutive is 1/35

Solution:

Consecutive numbers can be

(1, 2 ,3) , (2, 3, 4) , (3, 4, 5) , (4, 5, 6) ,(5, 6, 7) , (6, 7, 8) , (7, 8, 9) , (8, 9, 10) ,(9, 10, 11) , (10, 11, 12) ,(11, 12, 13) , (12, 13, 14) and (13, 14, 15)

13 Combination

And each combination can be 3 x 2 x 1 = 6 ways

Total possible = 13 x 6 = 78

Total Combinations = 15 x 14 x 13 = 2730

$Probability = \frac{78}{2730}\\\\Probability = \frac{1}{35}$

Thus the Probability that all three numbers are consecutive is 1/35

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