Probability that A Person is Healthy

If a person is healthy. he has a 20% \text {20\%} chance of being greater than 70 70 years old. If a person is greater than 70 70 years old, he has an 85% \text {85\%} chance of being healthy. Suppose 15% \text {15\%} of the citizens in a city are greater than 70 years old. What is the probability that a randomly selected person is healthy? Correct to 2 2 significant figures.


The answer is 0.64.

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1 solution

Sunny Singh
Aug 9, 2020

Let P be the population

Above 70 yrs = 0.15*P

Out of this, healthy = 0.15* 0.85 * P -------- (1)

Let N be healthy

Above 70 yrs = 0.2*N ---------------------- (2)

From (1) and (2), 0.15* 0.85 * P = 0.2*N ------ (3)

Probability that a randomly selected person is healthy = N/P

Using (3), we have N/P = 0.15*0.85/0.2 = 0.6375

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