Question

Discrete Structures Mathematics

Answer 1

Answer:

a) 62.5%

b) 37.5%

c) 4.3%

d) 71%

Step-by-step explanation:

A=1: component from the 1st factory

A=2: component from the 2nd factory

X=0: component OK

X=1: component defective

a) P(A=1)=100/160=0.625=62.5%

b) P(A=2)=60/160=0.375=37.5%

c) P(X=1) = P(X=1 & A=1) + P(X=1 & A=2) = P(X=1|A=1).P(A=1) + P(X=1|A=2).P(A=2) = 0.04*100/160 + 0.05*60/160 = 0.025 + 0.1875 = 0.04375 = 4.3%

d) Based on Bayes’ theorem:

P(A=1|X=1) = P(X=1|A=1).P(A=1)/P(X=1) = 0.05*(100/160)/0.04375 = 5/7 = 0.71 = 71%