Three numbers are chosen from 1 to 30. The probability that they are not consecutive, is
Answer & explanation
Correct answer: option 2
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).
∴ Number of elementary events in which three numbers are consecutive is 28.
Probability that the numbers are consecutive $=\frac{28}{^{30}C_3}=\frac{1}{145}$
Hence, required probability = $1-\frac{1}{145}=\frac{144}{145}$