1 - True/False: You are more likely to get a pattern of HTHHHTHTTH than HHHHHHHH
ID: 3206917 • Letter: 1
Question
1 - True/False: You are more likely to get a pattern of HTHHHTHTTH than HHHHHHHHTT when you flip a coin 10 times.
2 - True/False: Suppose that at your regular physical exam you test positive for a relatively rare disease. You will need to start taking medicine if you have the disease, so you ask your doc- tor about the accuracy of the test. It turns out that the test is 98% accurate. The probability that you have Disease X is therefore 0.98 and the probability that you do not have it is .02. Explain your answer.
Explanation / Answer
1.
False: Explanation: The probability of head or toss is 0.5 in a coin and any specific combination has probability of (0.5)^10 when the coin is flipped 10 times
Suppose that at your regular physical exam you test positive for Disease X. Although Disease X has only mild symptoms, you are concerned and ask your doctor about the accuracy of the test. It turns out that the test is 95% accurate. It would appear that the probability that you have Disease X is therefore 0.95. However, the situation is not that simple.
For one thing, more information about the accuracy of the test is needed because there are two kinds of errors the test can make: misses and false positives. If you actually have Disease X and the test failed to detect it, that would be a miss. If you did not have Disease X and the test indicated you did, that would be a false positive. The miss and false positive rates are not necessarily the same. For example, suppose that the test accurately indicates the disease in 99% of the people who have it and accurately indicates no disease in 91% of the people who do not have it. In other words, the test has a miss rate of 0.01 and a false positive rate of 0.09. This might lead you to revise your judgment and conclude that your chance of having the disease is 0.91. This would not be correct since the probability depends on the proportion of people having the disease. This proportion is called the base rate.
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