# 8.8.1. Probability

A life insurance company studied a sample of 5 000 men between the ages of 40 and 50 years old. It has been found that out of this sample, 25 men had died in the span of one year. If the company signed life-insurance contracts with 60 000 men between 40 and 50 years old, how many death benefits are expected to be paid in the span of a year?

• A 300
• B
15 000
• C
1 200
• D 250

### Example

A life insurance company studied a sample of 5 000 men between the ages of 40 and 50 years old. It has been found that out of this sample, 25 men had died in the span of one year. If the company signed life-insurance contracts with 60 000 men between 40 and 50 years old, how many death benefits are expected to be paid in the span of a year?

### Solution

Step 1: Find the probability of a man dying at an age between 40 and 50 within the span of one year.

Divide the number of men in the sample who died in the span of one year by the total number of men in the survey.

Step 2: Find the expected number of death benefits to be paid in a year.

Multiply the number of men between the ages of 40 and 50 with life-insurance contracts by the probability that a man in this age range will die in the span of the year.

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