Q#46: Life Expectancy

Suppose you’re analyzing a population of 100,000 people, and you’re trying to understand life expectancy. Within this population of 100,000 people, 75% can expect to live to the age of 70, while 45% can expect to live to age 80. Given that a person is 70, what is the probability that they live to the age 80?

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ANSWER

This question tests our understanding of statistics and probability, specifically Bayes’s Theorem.

Bayes’s Theorem defines conditional probability as P(A|B) [probability of A given B] = P(B|A)*P(A)/P(B). Using this formula we have P(Live to 80 | Live to 70) = P(Live to 70| Live to 80)*P(Live to 80)/P(Live to 70). We know that P(Live to 70| Live to 80) is 1, because if you have made it to 80 u must have passed 70. Furthermore, we are given P(Live to 80) and P(Live to 70) as .75 and .45 respectively. Thus, the answer:

P(Live to 80 | Live to 70) = 1*0.45/0.75 = 0.6