Answer: 0.4278
Step-by-step explanation:
Binomial probability formula :-
[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex], 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 :-
[tex]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[/tex]
