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?

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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(52852) About Me  (Show Source):
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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?
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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) = C%5B3%5D%5E2%2Ap%5E2%2A%281-p%29%5E%283-2%29 = 3%2A0.8%5E2%2A0.2%5E1 = 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) = 0.8%5E3 = 0.512.    ANSWER

Solved in full.