There are three machines that produce pencils in my factory. Machine A produces defective pencils 3% of the time, machine B produces defective pencils 6% of the time, and machine C produces defective pencils 12% of the time. Of the total output from these machines, 80% of the produced pencils are from machine A, 15% are from machine B, and only 5% are from machine C. One pencil is chosen at random from the daily production. What is the prior probability that the pencil came from machine A? What is the prior probability that the pencil came from machine B? What is the prior probability that the pencil came from machine C?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
There are three machines that produce pencils in my factory. Machine A produces defective pencils 3% of the time, machine B produces defective pencils 6% of the time, and machine C produces defective pencils 12% of the time. Of the total output from these machines, 80% of the produced pencils are from machine A, 15% are from machine B, and only 5% are from machine C. One pencil is chosen at random from the daily production.
- What is the prior
probability that the pencil came from machine A? - What is the prior probability that the pencil came from machine B?
- What is the prior probability that the pencil came from machine C?
- If, upon inspection, the pencil is found to be defective, what is the revised probability that it came from machine A?
- If, upon inspection, the pencil is found to be not defective, what is the revised probability that it came from machine B?
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