Question

Two socks are selected at random from a draw of loose socks- there are 4 green socks and 6 yellow socks

Answer 1

Using the hypergeometric distribution, it is found that there is a 0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.

What is the hypergeometric distribution formula?

The formula is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

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

The parameters are:

• x is the number of successes.

• N is the size of the population.

• n is the size of the sample.

• k is the total number of desired outcomes.

In this problem, we have that the values of the parameters are:

N = 10, k = 4, n = 2.

The probability that both are green is P(X = 2), hence:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 2) = h(2,10,2,4) = \frac{C_{4,2}C_{6,0}}{C_{10,2}} = 0.1333$

0.1333 = 13.33% probability that two of the socks will both be green if the socks are drawn without replacement.

More can be learned about the hypergeometric distribution at brainly.com/question/24826394

#SPJ1