Reference no: EM13966618
1. Suppose that 30 percent of computer owners use a Macintosh, 50 percent use Windows, and 20 percent use Linux. Suppose that 65 percent of the Mac users have succumbed to a computer virus, 82 percent of the Windows users get the virus, and 50 percent of the Linux users get the virus. We select a person at random and learn that her system was infected with the virus. What is the probability that she is a Windows user?
2. A box contains 5 coins and each has a different probability of showing heads. Let p1,..., p5 denote the probability of heads on each coin.
Suppose that
p1 = 0, p2 = 1/4, p3 = 1/2, p4 = 3/4 and p5 = 1.
Let H denote "heads is obtained" and let Ci denote the event that coin i is selected.
(a) Select a coin at random and toss it. Suppose a head is obtained. What is the posterior probability that coin iwas selected (i = 1,..., 5)? In other words, ?nd P(Ci|H) for i = 1,..., 5.
(b) Toss the coin again. What is the probability of another head? In other words ?nd P(H2|H1) where Hj = "heads on toss j."
Now suppose that the experiment was carried out as follows: We select a coin at random and toss it until a head is obtained.
(c) Find P(Ci|B4) where B4 = "?rst head is obtained on toss 4."
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Determine how the health care provider
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Simulation and compare the average
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Percent of computer owners use a macintosh
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Describe the sample space
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