Question

It is known that is certain prescription drug produces undesirable side effects in 35% of all patients who use it. Among a random sample of eight patients using the drug find the probability that at least three have undesirable side effects

Answer 1

Answer: 0.4278

Explanation:

Binomial probability formula :-

`P(X)=^nC_xp^x(1-p)^(n-x)`, here P(X) is the probability of getting success in x trials , n is total trials and p is the probability of getting success in each trial.

Given : The probability of undesirable side effects = 0.35

Sample size : n=8

The probability that at least three have undesirable side effects will be :-

`P(X\geq3)=P(X<3)\\\\=P(0)+P(1)+P(2)\\\\=^8C_0(0.35)^0(0.65)^(8)+^8C_1(0.35)^1(0.65)^(7)+^8C_2(0.35)^2(0.65)^(6)\\\\=(0.65)^(8)+8(0.35)^1(0.65)^(7)+(28)(0.35)^2(0.65)^(6)=0.42781365707\approx0.4278`