practice_Midterm1

# practice_Midterm1 - ISyE 2027B Fall 2010 Probability with...

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Probability with Applications Dr. Polly B. He Practice Midterm 1 You have 50 minutes to complete the exam. In order to get partial credit, you should show clearly the steps of your work. Leave your answer in the form of e - 1 , ( 5 3 ) , etc . Problem 1 (20 points) A monkey at a typewriter types each of the 26 letters of the alphabet exactly once, the order being random. (a) Deﬁne a suitable sample space. (b) What is the probability that the word “Hamlet” appears somewhere in the string of letters? Problem 2 (25 points) A person is diagnosed with an uncommon disease. There is a 1% chance of getting it. Use the letter D for the event “the person has the disease” and T for “the test says no”. It is known that the test is imperfect: P ( T | D ) = 0 . 98 and P ( T c | D c ) = 0 . 95. Given that the test is positive, what is the probability that the person really has the disease? 1

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practice_Midterm1 - ISyE 2027B Fall 2010 Probability with...

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