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# Probability watch

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1. Ok got a problem

On a TV game show contestants have to complete a particular task. Suppose that the time taken for a
typical contestant to complete the task is random variable, Z » Exp(1/2). That is, Z has probability
density function:
fZ(z) = (e^−z/2)/2 for z > =0
0 otherwise.
An individual is deemed to have failed if they take in excess of 3 minutes to complete the task.
a) Calculate the probability that a typical contestant fails to complete the task in 3 minutes.

b) Calculate the probability that a contestant takes over 2 minutes to complete the task given that
they do not fail. Assuming that the times taken by different contestants to complete the task are independent.

c) Calculate the probability that out of a group of 6 contestants, two contestants fail to complete the

d) Calculate the probability that none of the 6 contestants fail to complete the task given that the
first three contestants don’t fail.

e) Calculate the mean and variance for the number of contestants required until a failure occurs.

f) Find the approximate probability that out of 200 contestants there is between 40 and 50 failures
(inclusive).

Right a

the probability is 0.2231 got this by integrating the function etc

b Probaiblity is 0.6488 got this by integrating between 2 and 3 and then diving by the probability of 3

c) 0.2720 i did x is bin(6,0.2231)

but from then on I am stuck on D any solutions?
2. Part d) If the first three don't fail, then all you need is the probability that the next three don't fail, and as they are independent, this equals the probability that one doesn't fail, cubed.

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Updated: January 26, 2009
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