If a person is healthy. he has a 20% chance of being greater than 70 years old. If a person is greater than 70 years old, he has an 85% chance of being healthy. Suppose 15% of the citizens in a city are greater than 70 years old. What is the probability that a randomly selected person is healthy?
+23252 Let's say that there are 10,000 persons in the city.
Since 15% of the citizens are greater than 70 years old:
15% of 10,000 = 0.15 x 10,000 = 1500 persons are older than 70
and 8500 persons are younger than 70.
Since 85% of the persons older than 70 are healthy:
85% of 1500 = 0.85 x 1500 = 1275 persons older than 70 are healthy
and 225 persons older than 70 are not healthy.
Since 20% of the heathy person are greater than 70, this means that 80% of the healthy persons are younger
than 70. Since 80% is 4 times as great as 20%, there are 4 times as many healthly persons younger than
70 than those older than 70:
4 x 1275 = 5100 persons younger than 70 who are healthy.
Total number of healthy persons: 1275 + 5100 = 6375
Total number of persons: 10,000.
Probability of selecting a healthy person at random: 6375 / 10000 = 0.6375
