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

Answer:

$P(X=3)$

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

Step-by-step 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:

$nCx=\frac{n!}{(n-x)! x!}$

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