Question

A study conducted at a certain high school shows that 72% of its graduates enroll at a college. Find the probability that among 4 randomly selected graduates, at least one of them enrolls in college.

Answer 1

`P(X \geq 1) =1-P(X<1) =1-P(X=0)`

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

`P(X=0)=(4C0)(0.72)^0 (1-0.72)^(4-0)=0.00615`

And replacing we got:

`P(X \geq 1) = 1-0.00615 = 0.99385`

Explanation:

Let X the random variable of interest "number of graduates who enroll in college", on this case we now that:

`X \sim Binom(n=4, p=0.72)`

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!)`

We want to find the following probability:

`P(X \geq 1)`

And we can use the complement rule and we got:

`P(X \geq 1) =1-P(X<1) =1-P(X=0)`

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

`P(X=0)=(4C0)(0.72)^0 (1-0.72)^(4-0)=0.00615`

And replacing we got:

`P(X \geq 1) = 1-0.00615 = 0.99385`