Question

a trial drug is 45% effective at fighting a disease. if five people use the drug what is the probability that the drug will be effective for exactly three of them

Answer 1

To solve the question we use the binomial distributions formula given by:
P(x)=[(n!/(x!(xn-x)!))(p^x(1-p)^(n-x)
where:
P=effectiveness of the drug
n=Total sample
Thus probability of obtaining 3 positive cases out of 5 will be obtained by plugging our values in the formula, we shall have:
(5!/(3!(5-3)!))(0.45^3×(1-0.45)^(5-3))
but
5!/(3!(5-3)!)=10
also:
(0.45^3×(1-0.45)^(5-3))
=0.028
thus
P(x)=10×0.028=0.28

Answer: 0.28