Question

The probability that a patient recovers from coronavirus is 97%. What is the probability that a) all of the next 4 patients who are infected by the virus recover? b) exactly 3 of the next 4 patients who are infected by the virus recover? 7 A В І iii III & c?

Answer 1

Solution:
Given in the question
P(A patient recovers from coronavirus) = 0.97
Number of sample (n) = 4
Solution(a)
we need to calculate probability that all of the next 4 patients who are infected by the virus recover, here we will use binomial probability distribution which can be calculated as
P(X=n | N,p) = NCn*(p^n)*(1-p)^(N-n)
P(X=4) = 4C4 * (0.97^4)*(1-0.97)^(4-0) = 1 * 0.8853 * 1 = 0.8853
So there is 88.53% probability that all of the next 4 patients who are infected by the virus recover.
Solution(b)
we need to calculate probability that exactly 3 of the next 4 patients who are infected by the virus recover
P(X=3) = 4C3*(0.97^3)*(1-0.97)^(4-3) = 4 * 0.9127 * 0.03 = 0.1095
So there is 10.95% probability that exactly 3 patients who are infected by the virus recover.