Suppose the number of admissions to the emergency room at a

Suppose the number of admissions to the emergency room at a small hospital follows a Poisson distribution, but the incidence rate changes on different days of the week. On a weekday, there are on average 2 admissions per day, while on a weekend there is on average one admission per day.

1. What is the probability of at least one admission on a Wednesday?

2. What is the probability of at least one admission on a Saturday?

Solution

1)

Note that

P(at least one) = 1 - P(0)

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

Thus,

P(at least one) = 1 - 0.135335283 = 0.864664717 [ANSWER]

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2)

Note that

P(at least one) = 1 - P(0)

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 =    1      
          
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.367879441

Thus,

P(at least one) = 1 - 0.367879441 = 0.632120559 [ANSWER]