Meg has a bucket of plastic balls. Exactly 20% of these balls are yellow, and the rest are white. Some of the balls have a star on them. Exactly 6% of the balls are yellow and have a star on them. Meg will randomly draw 1 ball from the bucket. If the drawn ball is yellow, what is the probability that it will have a star on it?

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Suppose the number of balls in the bucket is \(x\). Then the number of yellow balls is \(0.2x\).

The number of yellow balls with stars on them is \(0.06x\).

Therefore, the probability that you will get a star on the yellow ball drawn is:

$$ P = \frac{\text{yellow balls with stars}}{\text{yellow balls}} $$ $$ = \frac{0.06x}{0.2x} = \frac{0.06}{.2}$$ $$ = \frac{30}{100} =\boxed{0.300} $$

Use the conditional probability equation, which is a generalization of approach 1:

$$ P(A|B) = \frac{P(A\cap B)}{P(B)} $$ $$ P(\text{star}|\text{yellow}) = \frac{P(\text{yellow and star})}{P(\text{yellow})} $$