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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 Spring '11
 a
 Operations Research, Probability, Probability theory, Exponential distribution, Don

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