A) This problem requires careful attention to the sequence of events. If you fli

Question

A)This problem requires careful attention to the sequence of events. If you flip a coin 3 times, the probability of getting the sequence HTH is identical to the probability of getting HTT (1/8). Let’s make this situation a little more interesting. Suppose you are going to flip a coin until you get the sequence HTH. Say this takes you x flips. Then, suppose you are going to flip the coin until you get the sequence HTT. Say this takes you z flips. On average, how will x compare to z? Will it be bigger, smaller, or equal? Explain why.     

B)Here's a three part puzzler that requires careful identification of the sequence of events.
1. Your friend has two children. What is the probability that both are girls?
2. Your friend has two children. You know for a fact that at least one of them is a girl. What is the probability that the other one is a girl?
3. Your friend has two children. One is a girl named Florida. What is the probability that the other child is a girl?     

C)Breast cancer affects .8 percent of the female population between 40 and 50 years of age. There are two kinds of positive test results: true (you have it) and false positives (the test indicates you do have it, but your really do not). Mammograms are 90% accurate at spotting people who have breast cancer (true positive), and are 93% (true negative) accurate at spotting people who do not. What are the false negative and false positive accuracies? If your patient tests positive for breast cancer, whether a true or false positive, compute the probability that she indeed has the disease? This is a conditional probability problem, the condition being test positive. The Course Content Session 3 Lecture beginning p. 13 provides an intuitive approach.

Explanation / Answer

HTT will take fewer throws, or z<x

Brief explanation:

Suppose you throw the sequence "HT". In either version, the following throw has a 50/50 chance of ending the game. If it does not end the game, then in the HTH game, you just threw a T, so you have to start over. In the HTT game, you just threw an H, so you are already one throw into a possible next winning sequence.

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