In a primary care clinic 25 of patients who have appointment

In a primary care clinic, 25% of patients who have appointments fail to show up. Each clinic session has 10 scheduled appointments. What is the probability that all patients show up? In a week, there are 10 clinical sessions. How many patients would you expect to fail to show up?

Solution

Here,

p(doesn\'t how up) = 0.25
p(show up) = 1-0.25 = 0.75

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a)

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 =    10      
p = the probability of a success =    0.75      
x = the number of successes =    10      
          
Thus, the probability is          
          
P (    10   ) =    0.056313515 [ANSWER]

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b)

E(don\'t show up) = 10*0.25 = 2.5 [ANSWER]