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

Answer:

$P(X \geq 1) =1-P(X$

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:

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

Step-by-step 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:  

$nCx=\frac{n!}{(n-x)! x!}$  

We want to find the following probability:

$P(X \geq 1)$

And we can use the complement rule and we got:

$P(X \geq 1) =1-P(X$

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:

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