Hello, horan!

Let = "4 different colors" . . .and = "at least one yellow"Suppose you have an urn with 2 yellow balls, 3 red balls, 6 white balls, and 12 blue balls.

You randomly draw 4 balls from the urn without replacement.

Given that at least one of the balls is yellow,

what is the probability that all 4 balls will be different colors?

According to Bayes' Theorm, we want . .[1]

There are: . possible drawings.

Numerator

As you pointed out:

The number of ways to get 4 colors is: . ways.

Hence: .

Denominator

The opposite of "at least 1 yellow" is "yellow."no

There are: . ways to get no yellows.

So there are: . ways to get at least one yellow.

Hence: .

Substitute into [1]: .