Question

"The chance that a person selected at random has blue eyes is 16%. Two people are chosen at random (and are independent of each other). Find the probability at least one of them does not have blue eyes. Round your answer to 4 decimal places."

Answer 1

Answer:

$P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256$

And replacing we got:

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

Step-by-step explanation:

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

$X \sim Binom(n=2, p=1-0.16=0.84)$

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 can find this probability:

$P(X \geq 1)$

And we can solve this probability like this:

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

And if we use the probability mass function we got:

$P(X=0)=(2C0)(0.84)^0 (1-0.84)^{2-0}=0.0256$

And replacing we got:

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