A chemical engineer is interested in determining whether a certain trace impurity is present in a product. An experiment has a probability of .80 of detecting the impurity if it is present. The probability of not detecting the impurity if it is absent is .90. The prior probabilities of the impurity being present and being absent are .40 and .60, respectively. Three separate experiments result in only two detections. What is the posterior probability that the impurity is present?
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.
A chemical engineer is interested in determining whether a
certain trace impurity is present in a product. An experiment
has a probability of .80 of detecting the impurity if it is
present. The probability of not detecting the impurity if it is
absent is .90. The prior probabilities of the impurity being
present and being absent are .40 and .60, respectively. Three
separate experiments result in only two detections. What is
the posterior probability that the impurity is present?
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