Discrete structures mathematics
two different factories both produce a certain automobile part. the probability that a component from the first factory is defective is 4%, and the probability that a component from the second factory is defective is 5%. in a supply of 160 of the parts, 100 were obtained from the first factory and 60 from the second factory.
(a) what is the probability that a part chosen at random from the 160 is from the first factory?
(b) what is the probability that a part chosen at random from the 160 is from the second factory?
(c) what is the probability that a part chosen at random from the 160 is defective?
(d) if the chosen part is defective, what is the probability that it came from the first factory?

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%

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )