Practicing Success
Three numbers are chosen from 1 to 30. The probability that they are not consecutive, is |
$\frac{142}{145}$ $\frac{144}{145}$ $\frac{143}{145}$ $\frac{1}{145}$ |
$\frac{144}{145}$ |
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 = $1-\frac{1}{145}=\frac{144}{145}$ |