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
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
