SOLUTION: Michael is one of five contestants entered in three races to be run on a five-lane track. If in each race the runners are assigned to the lanes at random, what is the probability t

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Question 129297: Michael is one of five contestants entered in three races to be run on a five-lane track. If in each race the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane at least once?
I know that the total number of possible outcomes is 5!, so I assume this to be the starting denominator.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Michael is one of five contestants entered in three races to be run on a five-lane track. If in each race the runners are assigned to the lanes at random, what is the probability that Michael will be assigned to the inside lane at least once?
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P(he is assigned to any particular lane) = 1/5 = p
There are three races so n=3
Since you want at least one succes use P(at least one) = 1- P(no successes)
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P(he get assigned to the inside lane at least once ) = 1- P(he does not
get assigned to lane one in all three races) = 1- (4/5)^3 = 0.488
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Cheers,
Stan H.