What is the probability of surviving?

Actuaries use a shorthand method to express these probabilities: tpx, which is the probability that a person age 'x' will survive another 't' years. So if 10p40 = 0.95, that means a 40-year-old has a 95% chance of surviving another 10 years.

cia-ica.ca - The Probability of Survival - Canadian Institute of Actuaries

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The Probability of Survival

What is the chance that you will live to be 75 years old? 100 years old? 120 years old?

We don’t know for sure, but actuaries need to be able to estimate these probabilities. For example, an actuary working on a pension plan will estimate how many people are expected to live to a certain age (age 65, 66, 67, and so on). This is because they need to calculate how much money should be set aside today to provide for all those pension payments in the future, because a pension is paid as long as the recipient is still alive.

How do actuaries make these estimates, since nobody knows for sure how long they are going to live?

They do this by studying large amounts of data. For example, an actuary may collect historical records on thousands of individuals. By looking at how many of those individuals were still alive at a certain age, they can determine their probabilities of survival. The more data they can collect, the more accurate their estimates are going to be. Actuaries also look at the difference in expected survivorship between men and women, people who are in good health and those who are not, and a number of other different factors. Actuaries use a shorthand method to express these probabilities: t p x , which is the probability that a person age ‘x’ will survive another ‘t’ years. So if 10 p 40 = 0.95, that means a 40-year-old has a 95% chance of surviving another 10 years. In the Million Dollar Problem, you will need to use statistics like these to help determine the fee that should be charged. Here are some sample values for you to use—make sure you choose the right one!

16 p 16 = 0.90

74 p 16 = 0.07

90 p 16 = 0.03

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