Question

A die is rolled 12 times find the probability of rolling exactly 12 ones

Answer 1

probability of rolling exactly 12 ones is 1/6^12

Answer 2

`P(X=12)=(12C12)((1)/(6))^12 (1-(1)/(6))^(12-12)=4.59x10^(-10)`

Explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We assume that the die is fair and the probability of obatin a one is 1/6.

Let X the random variable of interest, on this case we now that:

`X \sim Binom(n=12, p=1/6)`

And we want to find this probability:

`P(X=12)`

And if we replace we got:

`P(X=12)=(12C12)((1)/(6))^12 (1-(1)/(6))^(12-12)=4.59x10^(-10)`