Question

3. (25 pts) Bob has recently been hired by a shop downtown to help customers with various computer-related problems. Lately, two different viruses have been bugging many customers: Dummy and Smarty. It is estimated that about 65% of the customers with virus problems are bothered by Dummy and the remaining 35% by Smarty. If the computer is infected by Dummy, Bob has a 90% chance of fixing the problem. However, if the computer is infected by Smarty, this chance is only 70%.A virus-infected computer is randomly selected from the shop. A. Draw a tree diagram that models the information given above. Identify each branch with an event and a probability B. Find the probability a randomly selected infected computer can be fixed by Bob. C. Suppose it was known that a particular computer was fixed by Bob. What is the probability that it was infected by virus Dummy?

Answer 1

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A 09 0.1 Jin ho Dummy 0.65 0.35 Smanty 0.7 cho no you b) let F= event that rand domly selected infected computer is frued by Bo b. in P(F). Plata +P (F/Smarty) P (smarty Og x0.65 t 0.7x 0:35 (F) 0.83

(o? P(Rummy fined) = f( Dummy F) P( El Dummy). P (Dummy) ?CF2 fusing Bayes Theorem ار 0.9..0.6.5 0.7048 o og 3