In a certain clinical study, 15% of participants were classified as heavy smokers, 25% as light-smokers, and the rest as non-smokers. at the end of the study, the death rates of the heavy and light smokers were 5 and 3 times that of non-smokers, respectively. what is the probability that a randomly selected participant who died by the end of the study was a non-smoker?

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.

Step-by-step explanation:

We have the following probabilities:

A 15% probability that a participant is classified as a heavy smoker.

A 25% probability that a participant is classified as a light smoker.

A 100% - 25% - 15% = 60% probability that a participant is classified as a non smoker.

A x% probability that a non smoker dies.

A 3x% probability that a light smoker dies.

A 5x% probability that a heavy smoker dies.

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

This problem is:

What is the probability of the participant being a non-smoker, given that he died?

P(B) is the probability that the participant is a non smoker. So

P(A/B) is the probability that the participant dies, given that he is a non smoker. So:

P(A) is the probability that the participant dies:

is the probability that a heavy smoker is selected and that he dies. So:

is the probability that a light smoker is selected and that he dies. So:

is the probability that a non-smoker is selected and that he dies. So:

The probability that a participant dies is:

The probability of the participant being a non-smoker, given that he died, is:

There is a 28.57% probability that a randomly selected participant who died by the end of the study was a non-smoker.