Question

Suppose that 45% of students in a college have a smart phone. If you select three students at random, what is the probability that all three have a smart phone? Give your answer as a decimal (to at least 3 places) or fraction

Answer 1

`P(X=3)`

And we can use the probability mass function and we got:

`P(X=3)=(3C3)(0.45)^3 (1-0.45)^(3-3)=0.091`

Then the probability that all three have a smart phone is 0.091

Explanation:

Let X the random variable of interest "number of students with smartphone", on this case we now that:

`X \sim Binom(n=3, p=0452)`

The probability mass function for the Binomial distribution is given as:

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

Where (nCx) means combinatory and it's given by this formula:

`nCx=(n!)/((n-x)! x!)`

And we want to find this probability:

`P(X=3)`

And we can use the probability mass function and we got:

`P(X=3)=(3C3)(0.45)^3 (1-0.45)^(3-3)=0.091`

Then the probability that all three have a smart phone is 0.091