Using geometric distribution, the probability that the first person has an injection-site reaction, but the next two do not is 0.087131.
Geometric distribution is "a discrete probability distribution that represents the probability number of successive failure before a success obtained in a Bernoulli trial".
According to the question,
Patients experience injection-site reactions with current needle is 11%.
Number of people receive injections with this type of needle is 3.
The probability mass function of Geometric distribution (PMF) is given as
[tex]P(1 - p)^(x-1)[/tex].
P = 11 % = 0.11
In order to find the probability that the first person has an injection-site reaction, but the next two do not
= [tex]0.11(1-0.11)^(3-1)[/tex]
= [tex]0.11(0.89)^2[/tex]
=0.11(0.7921)
=0.087131
Hence, using geometric distribution, the probability that the first person has an injection-site reaction, but the next two do not is 0.087131.
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