Case Study: How Likely Are You to Live to Age 100? The following table is a life table, reproduced from the chapter introduction. With an understanding of some basic concepts of probability, one can use the life table to compute the probability that a person of a given age will still be alive a given number of you from now. Life insurance companies use this information to determine how much to charge for life insurance policies. United States Life Table, Total Population Age Interval Proportion Surviving Age Interval Proportion Surviving 0-10 0.99123 50-60 0.94010 10-20 0.99613 60-70 0.86958 20-30 0.99050 70-80 0.70938 30-40 0.98703 80-90 0.42164 40-50 0.97150 90-100 0.12248 Source: Centers for Disease Control and Prevention The column labeled "Proportion Surviving" gives the proportion of people alive at the beginning of an age interval who will still be alive at the end of the age interval. For example, among those currently age 20, the proportion who will still be alive at age 30 is 0.99050, or 99.050%. We will begin by computing the probability that a person lives to any of the ages 10, 20, ..., 100. The first number in the column is the probability that a person lives to age 10. So P (Alive at age 10) = 0.99123 The key to using the life table is to realize that the rest of the numbers in the "Proportion Surviving" column are conditional probabilities. They are probabilities that a person is alive at the end of the age interval, given that they were alive at the beginning of the age interval. For example, the row labeled "20-30" contains the conditional probability that someone alive at age 20 will be alive at age 30: P (Alive at age 30 | Alive at age 20) = 0.99050 In Exercises 1-5, compute the probability that a person lives to a given age. 1. From the table, find the conditional probability P (Alive at age 20 | Alive at age 10). 2. Use the result from Exercise 1 along with the result P (Alive at age 10) = 0.99123 to compute P (Alive at age 20). 3. Use the result from Exercise 2 along with the appropriate number from the table to compute P (Alive at age 30). 4. Use the result from Exercise 3 along with the appropriate number from the table to compute P (Alive at age 40). 5. Compute the probability that a person is alive at ages 50, 60, 70, 80, 90, and 100