Answer: (a)0.8145
(b) 0.99951875
Step-by-step explanation:
Binomial probability formula to find the probability of getting success in x trials :-
[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex] , where n is the total number of trials and p is the probability of success in each trial.
Given : The probability that the electronic production line yields satisfactory parts =0.95
The number of parts tested = 4
(a) The probability that all parts tested are satisfactory:-
[tex]P(4)=^4C_4(0.95)^4(0.05)^{0}=(0.95)^4=0.81450625\approx0.8145[/tex]
(b) The probability that at least two parts are satisfactory :-
[tex]P(x\geq2)=1-P(x\leq1)=1-(P(0)+P(1)))\\\\=1-(^4C_0(0.95)^0(0.05)^{4}+^4C_1(0.95)^1(0.05)^{3})\\\\=1-((0.05)^{4}+4(0.95)(0.05)^3)=0.99951875\approx0.9995[/tex]
