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homework2 - available options 4 Among a certain group of...

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1 EL 630: Homework 2 1. The four switches in the figure operate independently. Each switch is closed with probability p and opened with probability (1- p ). (a) Find the probability that a signal at the input will be received at the output (b) Find the conditional probability that switch S 4 is open given that the signal is received at the output. S 1 Input S 4 Output S 2 S 3 2. Three fair coins are tossed simultaneously 10 times. Find the probability that “2 heads and one tail” will show up (a) at most once (b) at least once. 3. Fifty people are asked to go from N.Y to L.A. They have the options to travel by car, train, bus or plane. What is the probability that 10 people travel by car, 5 by train, 8 by bus and the remaining decide to fly (Assume that each person independently makes the decision and randomly picks any one of the four
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Unformatted text preview: available options). 4. Among a certain group of people 5% are (professional) liers. A lie detector test on a lier is found to be positive with probability 0.94. If the test is administered to a non-lier, it is positive with probability 0.08. Given that the test is positive for a randomly picked person from that group, what is the probability that he is a lier ? 5. A coin is tossed an infinite number of times. Show that k heads are observed at the n th tossing, but not earlier equals . 1 1 k n k q p k n- --6. A fair die is rolled 6 times. Find the probability that one shows twice, three shows thrice and five shows once....
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