Question

Two flower seeds are randomly selected from a package that contains 8 seeds for red flowers and 9 seeds for white flowers. (Give your answer correct to three decimal places.)
(a) What is the probability that both seeds will result in red flowers?

Incorrect: Your answer is incorrect.


(b) What is the probability that one of each color is selected?


(c) What is the probability that both seeds are for white flowers?

Answer 1

Using the hypergeometric distribution, it is found that the probabilities are given as follows:

a) 0.2059 = 20.59%.

b) 0.5294 = 52.94%.

c) 0.2647 = 26.47%.

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, the parameters are as follows: N = 17, k = 8, n = 2.

Item a:

This probbility is P(X = 2), hence:

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

$P(X = 2) = h(2,17,2,2) = \frac{C_{8,2}C_{9,0}}{C_{17,2}} = 0.2059$

Item b:

This probbility is P(X = 1), hence:

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

$P(X = 1) = h(1,17,2,2) = \frac{C_{8,1}C_{9,1}}{C_{17,2}} = 0.5294$

Item c:

This probbility is P(X = 0), hence:

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

$P(X = 0) = h(0,17,2,2) = \frac{C_{8,0}C_{9,2}}{C_{17,2}} = 0.2647$

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