IE143-LQ3reviewprobs - University of the Philippines...

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University of the Philippines – Diliman Department of Industrial Engineering and Operations Research IE 143 Long Quiz 3 Long Quiz 3 Review Problems 1. At each trial of a game, Don and Greg flip biased coins, simultaneously but independently. For each trial, the probability of heads is 0.6 and 0.7 for Don and Greg, respectively. a) Given that the flips on a particular trial resulted in 2 heads, find the expected number of additional trials up to and including the next trial on which 2 heads result. (+) b) Given that the flips on a particular trial resulted in at least one head, find the probability that Don flipped a head on that trial. (+) c) Starting from a trial on which no heads result, find the probability that Don’s next flip of a head will occur before Greg’s next flip of a head. (+++) d) Given that Don receives $3 for each head he flips, and Greg receives $4 for each head he flips, find the expected total amount of money earned by the two players during the first ten trials. (+) 2. To cross a single lane of moving traffic, we require at least five minutes of no cars. Successive car interarrival times are independently and exponentially distributed with mean of 3 minutes. If an interval between successive cars is longer than 5, we say that the interval represents a single opportunity to cross the lane. Assume that car lengths are small relative to intercar spacing and that our experiment begins the instant after the zeroth car goes by. Determine the probability that: a) We can cross the first time just before the 5 th car goes by. (++) b) We shall have had exactly 6 opportunities by the instant the 20 th car goes by. (++) 3. Fred is giving out samples of dog food. He makes calls door to door, but he leaves a sample (one can) only
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This note was uploaded on 05/19/2011 for the course IE 2 taught by Professor A during the Spring '11 term at University of the Philippines Diliman.

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IE143-LQ3reviewprobs - University of the Philippines...

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