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 . .
There are: . possible drawings.
As you pointed out:
The number of ways to get 4 colors is: . ways.
The opposite of "at least 1 yellow" is "no yellow."
There are: . ways to get no yellows.
So there are: . ways to get at least one yellow.
Substitute into : .