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?

Guest Aug 7, 2020

#1**+1 **

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

geno3141 Aug 7, 2020