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cp102

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1.Your friend is playing Monopoly and is in desperate straits. He is cashless and has just landed in jail. He must either roll a double to get out free or pay $50 after his third attempt of not getting doubles or be kicked out. He is making no money while in jail. What is the likelihood that he will roll doubles by at least his third turn? Explain your conclusion.

2.As a public school teacher I am required to get a tuberculosis (TB) test every 5 years. This is done by inserting some kind of solution under the skin of my forearm. 48 hours later I’m to report to the nurse and have my TB test “read”. This involves seeing whether my forearm looks “normal” or is red and sploggy where they have injected me with that horrid concoction. Well, suppose that the test is 99% effective, that is, 99% of the time if a person that does not have TB, the test correctly shows negative. Looking up online, we learn from CDC that 5 out of every 10,000 people in the U.S have TB. We also earn that long term studies of this test show that only about 0.1% of people with TB show a false negative. So I go back 48 hours after being given the serum under my skin for a TB test. I can see myself that the spot on my arm is red and swollen. What is the probability that I actually have the disease? Support your conclusion.

3.Research suggests that about 24% of thirteen years olds in the US can pick out the state of Colorado on a political lined map of the country. Assume that this is true.

a. What is the probability that exactly 5 out of a sample of 12 thirteen-year-olds will be able to pick out Colorado on a map?

b. What is the probability that you must sample 5 or more thirteen-year-olds to find the first one who can pick out Colorado on a map?