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An health insurance company divides people into two classes (young and old). The company's statistics show that an old person will have health problems at some time within one year with probability 0.7, and a young person will have health problem in the same period with probability 0.3. Assume that 20% of the population is old and suppose that a new policyholder has an health problem within that year. What is the probability that he or she is old?

An health insurance company divides people into two classes (young and old). The company's statistics show that an old person will have health problems at some time within one year with probability 0.7, and a young person will have health problem in the same period with probability 0.3. Assume that 20% of the population is old and suppose that a new policyholder has an health problem within that year. What is the probability that he or she is old?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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An health insurance company divides people into two classes (young and old). The company's statistics show that an old person will have health problems at some time within one year with probability 0.7, and a young person will have health problem in the same period with probability 0.3. Assume that 20% of the population is old and suppose that a new policyholder has an health problem within that year. What is the probability that he or she is old?

Expert Solution
Step 1: Introduce the given information

Let,

A = Person is old.

Ac = Person is not old (that is, young).

B = Person have health problems.

According to the given information,

P(B | A) = 0.7

P(B | Ac) = 0.3

P(A) = 20% = 0.2

So, P(Ac) = 1-0.2 = 0.8

Using formula,

P left parenthesis X vertical line Y right parenthesis equals fraction numerator P left parenthesis Y vertical line X right parenthesis cross times P left parenthesis X right parenthesis over denominator P left parenthesis Y vertical line X right parenthesis cross times P left parenthesis X right parenthesis plus P left parenthesis Y vertical line X to the power of c right parenthesis cross times P left parenthesis X to the power of c right parenthesis end fraction

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