Question

in clinical trials a certain drugs has a 8% success rate of curing a known diseases. If 15 people are known to have the diseases, what is the probability that at least 2 are cured?

Answer 1

Let $X=$ the number of cured people: $X\sim Bin(n, p).$

Given $n=15, p=0.08, q=1-p=1-0.08=0.92.$

Then

$$P(X\geq2)=1-P(X=0)-P(X=1)$$

$$=1-\dbinom{15}{0}(0.08)^0(0.92)^{15-0}-\dbinom{15}{1}(0.08)^1(0.92)^{15-1}$$

$$\approx1-0.28629740407-0.37343139661$$

$$\approx0.340271$$