Chapter 8.4, Problem 59E

Medical research. In a random sample of $1,000$ people, it is found that $7\%$ have a liver ailment. Of those who have a liver ailment, $40\%$ are heavy drinkers, $50\%$ are moderate drinkers, and $10\%$ are nondrinkers. Of those who do not have a liver ailment, $10\%$ are heavy drinkers. $70\%$ are moderate drinkers, and $20\%$ are nondrinkers. If a person is chosen at random and he or she is a heavy drinker, what is the probability of that person having a liver ailment? What is the probability for a nondrinker?