3.) Consider the following two-way classification of 500 individuals: Prominent Wrinkles 95 Wrinkles Not Prominent 55 Heavy Smoker Light or Nonsmoker 100 250 One individual is selected at random. a.) Given that the individual is a heavy smoker, what is the probability that he/she has prominent wrinkles? b.) What is the probability that the selected individual is a heavy smoker or has prominent wrinkles?

3.

Given:

$\begin{array}{rcl}\mathrm{Total}& =& 500\\ \mathrm{Number} \mathrm{of} \mathrm{heavy} \mathrm{smokers}& =& 150\\ \mathrm{Number} \mathrm{of} \mathrm{light} \mathrm{or} \mathrm{nonsmoker}& =& 350\\ \mathrm{Number} \mathrm{of} \mathrm{prominent} \mathrm{wrinkles}& =& 195\\ \mathrm{Number} \mathrm{of} \mathrm{wrinkles} \mathrm{not} \mathrm{prominent}& =& 305\end{array}$

a)

The probability that he/she has prominent wrinkles given that the individual is a heavy smoker is obtained as below:

$\begin{array}{rcl}\mathrm{P}\left(\mathrm{Prominent} \mathrm{wrinkles}|\mathrm{heavy} \mathrm{smoker}\right)& =& \frac{\mathrm{P}\left(\mathrm{Prominent} \mathrm{wrinkles}\cap \mathrm{heavy} \mathrm{smoker}\right)}{\mathrm{P}\left(\mathrm{heavy} \mathrm{smoker}\right)}\\ & =& \frac{{\displaystyle \frac{95}{500}}}{{\displaystyle \frac{150}{500}}}\\ & =& \frac{95}{150}\\ & =& 0.6333\end{array}$

Thus, the probability that he/she has prominent wrinkles given that the individual is a heavy smoker is 0.6333.