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

Options

A. `(142)/(145)`
B. `(144)/(145)`
C. `(143)/(145)`
D. `(1)/(145)`

Answer

B

Explanation

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)`