Question

Assume there is probability of 0.36 that a U.S. soldier who served in the last decade has served in Iraq. If a soldier served in the last decade and was in Iraq, suppose there is a probability of 0.14 the person developed lung problems. However, if the soldier served in the last decade and was not in Iraq, suppose there is a 0.10 probability the person developed lung problems. If a soldier who served in the last decade developed lung problems, what is the probability the soldier served in Iraq?

Answer 1

0.440559

Explanation:

To find the probability of having a soldier from Iraq that had lung problems, we multiply the 2 probabilities, so 0.36*0.14 = 0.0504

The probability of a soldier serving not in Iraq and having lung problems is 0.64 (serving in Iraq is 0.36, so not serving in Iraq is 1 - 0.36 = 0.64) times 0.1 = 0.064.

If we sum up these two probabilities, we have the probability of a soldier having lung problems (0.0504+0.064 = 0.1144).

Now, to know the probability of a soldier with a lung problem having served on Iraq, we divide the probability of serving in Iraq and having lung problems (0.0504) by the probability of having lung problem (0.1144):

0.0504/0.1144 = 0.440559