Question

In a random sample of 1,000 people, it is found that 8.3% have a liver ailment. Of those who have a liver ailment, 8% are heavy drinkers, 65% are moderate drinkers, and 27% are nondrinkers. Of those who do not have a liver ailment, 14% are heavy drinkers, 42% are moderate drinkers, and 44% are nondrinkers. If a person is chosen at random, and he or she is a heavy drinker, what is the empirical probability of that person having a liver ailment?

Answer 1

To find the empirical probability of a person having a liver ailment given that they are a heavy drinker, we can use the information provided in the question. First, find the probability of being a heavy drinker with a liver ailment. Next, find the probability of being a heavy drinker without a liver ailment. Finally, divide the probability of being a heavy drinker with a liver ailment by the total probability of being a heavy drinker (with or without a liver ailment) to find the empirical probability.

Step-by-step explanation:

To find the empirical probability of a person having a liver ailment given that they are a heavy drinker, we can use the information provided in the question.

1. First, find the probability of being a heavy drinker with a liver ailment. This is 8% of the 8.3% who have a liver ailment: 8% * 8.3% = 0.664%.
2. Next, find the probability of being a heavy drinker without a liver ailment. This is 14% of the 91.7% who do not have a liver ailment: 14% * 91.7% = 12.838%.
3. Finally, divide the probability of being a heavy drinker with a liver ailment by the total probability of being a heavy drinker (with or without a liver ailment) to find the empirical probability: 0.664% / (0.664% + 12.838%) = 4.90%.

Therefore, the empirical probability of a person having a liver ailment given that they are a heavy drinker is 4.90%.