Question

) Suppose that a subset of five balls will be randomly selected from an urn containing amber, blue, and green balls. (a) If the urn initially contains 6 amber, 5 blue, and 4 green balls, what is the probability that all 5 balls selected will be the same color

Answer 1

Answer:

0.0023 = 0.23% probability that all 5 balls selected will be the same color

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the balls are selected is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

Desired outcomes:

Either 5 amber from a set of 6, or 5 blue from a set of 5. So

$D = C_{6,5} + C_{5,5} = \frac{6!}{5!1!} + \frac{5!}{5!0!} = 6 + 1 = 7$

Total outcomes:

5 balls selected from a set of 6 + 5 + 4 = 15. So

$T = C_{15,5} = \frac{15!}{5!10!} = 3003$

Probability:

$p = \frac{D}{T} = \frac{7}{3003} = 0.0023$

0.0023 = 0.23% probability that all 5 balls selected will be the same color