The probability that a hospital emergency room patient is allergic to the tetanu

Question

The probability that a hospital emergency room patient is allergic to the tetanus vaccine is 20%. If three strangers arrive at the hospital emergency room between midnight and 1 a.m., each admitted as patients and each needing the tetanus vaccine as a precaution, find the probability that among these three patients, at most 2 patients are allergic to the vaccine.

B) find the probability that among these three patients, exactly 1 patients are allergic to the vaccine.

Please show detailed solutions! Thank You!

Explanation / Answer

A)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    3      
p = the probability of a success =    0.2      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.992 [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 =    3      
p = the probability of a success =    0.2      
x = the number of successes =    1      
          
Thus, the probability is          
          
P (    1   ) =    0.384 [ANSWER]

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