Three numbers are chosen at random from numbers 1 to 30. Write the probability that the chosen numbers are consecutive.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
Three numbers are chosen at random from numbers 1 to 30. Write the probability that the chosen numbers are consecutive.
Three numbers are chosen at random from numbers 1 to 30. Write the probability that the chosen numbers are consecutive.
Let E denote the event that the chosen numbers are consecutive.
No of ways in which 3 numbers can be chosen out of 30 = 30C3
As we have to select 3 consecutive numbers, if we select 1 number other two are already selected.
As 29,30 can’t be selected because if they are selected we won’t be able to get 3 consecutive numbers.
∴ number of ways in which 3 consecutive numbers can be selected = number of ways in which 1 number can be chosen out of numbers from 1 to 28 = 28C1 ways
∴ P(E) = \(\frac{28}{^{30}C_3}\) = \(\frac{28\times3\times2\times1}{30\times29\times28}\) = \(\frac{1}{145}\)
Thus, P(E) = \(\frac{1}{145}\)