Question

An urn contains 5 red, 6 blue, and 8 green balls. If a set of 3 balls is randomly selected, what is the probability that each of the balls will be (a) of the same color?

Answer 1

As a fraction, the answer is exactly 86/969

In decimal form, the answer is approximately 0.08875

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Work Shown:

The assumption is that no replacements are made for each selection.

5 red, 6 blue, 8 green

5+6+8 = 19 total

A = P(3 red) = (5/19)*(4/18)*(3/17) = 10/969

B = P(3 blue) = (6/19)*(5/18)*(4/17) = 20/969

C = P(3 green) = (8/19)*(7/18)*(6/17) = 56/969

D = P(3 all same color)

D = A+B+C

D = 10/969 + 20/969 + 56/969

D = (10+20+56)/969

D = 86/969

D = 0.08875