The probability that the first four patients are elderly is 0.1504. The probability that exactly 2 out of 3-morning patients are elderly patients is 0.432
The probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
The given information is;
The proportion of the morning appointments that are with elderly patients = 60%
The number of patients in the appointments is 10 patients
The proportion of the morning appointments that are with non-elderly patients
= 100 - 60 = 40%
The binomial probability distribution is given as;
[tex]P(X =r ) = \left(\begin{array}{ccc}n\\r\end{array}\right)p^r (1-p)^{p-r}[/tex]
[tex]P(X =0)[/tex] = 0.000105
P(X =1) = 0.0016
P(X =2) = 0.01062
P(X = 3) = 0.0425
The probability that the first four patients are elderly
= 0.000105 + 0.0016 + 0.1062 + 0.0425
= 0.1504
The probability that exactly 2 out of 3-morning patients are elderly patients is given as
P(X =2) = 0.432
Learn more about the interpretation of probability here:
https://brainly.com/question/23024246
#SPJ2
