1. ## Probability

Need some help with this problem:

A nurse is to give Mr. Sean a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Sean will die is 1/3. If he does not get the pill, the probability that he will die is 3/4. Mr. Sean died. What is the probability that the nurse did not forget to give Mr. Sean the pill? What is the probability that Mr. Sean died and the nurse did not give him the pill?

Thank you!

2. You should use Bayes' Rule. Therefore, the answer is 1/2.

3. Originally Posted by eri123
Need some help with this problem:

A nurse is to give Mr. Sean a pill each day. The probability that the nurse forgets to administer the pill is 2/3. If he receives the pill, the probability that Mr. Sean will die is 1/3. If he does not get the pill, the probability that he will die is 3/4. Mr. Sean died. What is the probability that the nurse did not forget to give Mr. Sean the pill? What is the probability that Mr. Sean died and the nurse did not give him the pill?

Thank you!
Draw a tree diagram. Then it is easy to see that:

For the first, it follows from Bayes theorem that Pr(did not forget | died) = $\displaystyle \frac{\frac{1}{9}}{\frac{1}{9} + \frac{6}{12} } = ....$.

For the second, (2/3) (3/4) = 6/12.

Originally Posted by atalay
You should use Bayes' Rule. Therefore, the answer is 1/2.

4. Originally Posted by mr fantastic
Draw a tree diagram. Then it is easy to see that:

For the first, it follows from Bayes theorem that Pr(did not forget | died) = $\displaystyle \frac{\frac{1}{9}}{\frac{1}{9} + \frac{6}{12} } = ....$.

For the second, (2/3) (3/4) = 6/12.

5. Originally Posted by atalay
My answer to the second question is 1/2. However, Bayes Theorem is not used for the second question, it is only used for the first.

By saying use Bayes Theorem and then saying the answer is 1/2, your original reply implied that the answer to the first question is 1/2, which is wrong.