Answer to Question #338666 in Statistics and Probability for sadiya

Question

On an average 5% of the population in an area suffers from Diabetes. What is the probability that out of 7 persons chosen at random from this area with less than and equals to three suffer from the disease

Answer 1

Let $X=$ the number of persons suffer from the disease :$X\sim Bin(n, p).$

Given $n=7 p=0.05, q=1-p=0.95.$

$P(X\le)=P(X=0)+P(X=1)$

$+P(X=2)+P(X=3)$

$=\dbinom{7}{0}(0.05)^{0}(0.95)^{7-0}+\dbinom{7}{1}(0.05)^{1}(0.95)^{7-1}$

$\approx0.0002927$

$+\dbinom{7}{2}(0.05)^{2}(0.95)^{7-2}+\dbinom{7}{3}(0.05)^{3}(0.95)^{7-3}$

$=0.99980642188$