Question

A collection of 120 critical components is available for your use. It is generally known that the rate of occurrence of defects is 5% and that on the average 1 out of 20 will be defective. If you are to select 40 out of the 120 for use find the following probabilities using a) Binomial b) Hypergeometric and c) Poisson

Answer 1

Answer:a

a) 0.2777

b)0.3377

c)0.2707

Explanation:

binomial-

n=40

p=0.05

P ( X =2) = C(40,2)×0.05^2×(1-0.05)^38 = 0.2777 (answer)

hypergeometric-

total component,N=120 out of which 6 are defective and 114 are non defective

P(X=2)= C(6,2)×C (114,38)/C(120,40) =0.3377

Poisson-

Mean/Expected number of events of interest: λ = np=40×0.05 =2

P ( X =2 ) = e^-(2×2^2/2!)= 0.2707