Question

A die is rolled 5 times and a 5 or 6 is considered a success. Find the peobability of no success

Answer 1

0.1317 = 13.17% probability of no successes.

Explanation:

For each toss, there are only two possible outcomes. Either there is a success, or there is not. The probability of a success on a toss is independent of any other toss, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

In which
`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

And p is the probability of X happening.

A die is rolled 5 times.

This means that
`n = 5`

5 or 6 is considered a success.

2 out of 6 sides are successes, so:

`p = (2)/(6) = 0.3333`

Find the probability of no success:

This is P(X = 0). So

`P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)`

`P(X = 0) = C_(5,0).(0.3333)^(0).(0.6667)^(5) = 0.1317`

0.1317 = 13.17% probability of no successes.