Cavities And Candy
Say the probability I have a cavity is \(\frac{1}{4}\) and the probability I do not have a cavity is \(\frac{3}{4}\). If I have a cavity, then I eat candy with probability \(\frac{4}{5}\). If I do not have a cavity, then I eat candy with probability \(\frac{1}{3}\). Please answer in the form of a decimal with two significant digits.
What is the probability that I will eat candy?
By the Law of total Probability,
\(\Pr[\text{eat candy}]=\Pr[\text{eat candy}\;|\;\text{have cavity}]\cdot \Pr[\text{have cavity}]\)\( + \Pr[\text{eat candy}\;|\;\text{do not have cavity}]\cdot \Pr[\text{have cavity}]\)
\(= \frac{4}{5}\cdot\frac{1}{4}+\frac{1}{3}\cdot\frac{3}{4} = \frac{9}{20}\)