40% of the goods produced in a factory are produced on machine A, 50% on machine B and 10% on machine C. From the production on these machines, it is known that 4% of those in machine A, 5% of those in B and 3% of those in C are defective. a) The probability that one of the goods produced at random is defective, b) When the random good is known to be defective, find the probability that it was produced by machine A.
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.
40% of the goods produced in a factory are produced on machine A, 50% on machine B and 10% on machine C. From the production on these machines, it is known that 4% of those in machine A, 5% of those in B and 3% of those in C are defective.
a) The probability that one of the goods produced at random is defective,
b) When the random good is known to be defective, find the probability that it was produced by machine A.
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