A reservation service employs five information operators who

A reservation service employs five information operators who receive requests for information independently of one another, each according to a Poisson process with rate equal to two per minute. What is the probability that during a given 1-min period, the first operator receives no requests? What is the probability that during 2-minute period, exactly three of the five operators receive no request?

Solution

A)

Note that the probability of x successes out of n trials is          
          
P(x) = u^x e^(-u) / x!          
          
where          
          
u = the mean number of successes =    2      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.135335283 [ANSWER]

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B)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    5      
p = the probability of a success =    0.135335283      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.018532268 [ANSWER]