SOLUTION: The probability that a patient recovers from a delicate heart operation is 0.8. What is the probability that (a) exactly 2 of the next 3 patients who have this operation survive?

Question 1209576: The probability that a patient recovers from a delicate heart operation is 0.8. What is the probability that
(a) exactly 2 of the next 3 patients who have this operation survive?
(b) all of the next 3 patients who have this operation survive?
Answer by ikleyn(52858) (Show Source): You can put this solution on YOUR website!
.
The probability that a patient recovers from a delicate heart operation is 0.8.
What is the probability that
(a) exactly 2 of the next 3 patients who have this operation survive?
(b) all of the next 3 patients who have this operation survive?
~~~~~~~~~~~~~~~~~~~~~~~~

It is the binomial distribution problem.
The probability of success for any/each individual trial is p = 0.8.
So, apply the standard binomial distribution formulas for probabilities.

(a)  The number of trials n = 3;  the number of successful trials k = 2.

         P(n=3; k=2, p= 0.8) =  =  = 0.384.    ANSWER


(b)  The number of trials n = 3;  the number of successful trials k = 3.

         P(n=3; k=3;  p= 0.8) =  = 0.512.    ANSWER

Solved in full.

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