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Three numbers are chosen from 1 to 30. T...

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)`

Text Solution

Verified by Experts

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