8. Capacitors are made by 2 machines, M1 and M2. The probability that a capacitor is manufactured acceptably varies according to the machine. The probabilities are 0.9 and 0.95 respectively for machine M1 and M2. Machine M1 manufactures 80% of the capacitors. (a) Draw a tree diagram and attach the probabilities for every branch and outcome. (b) “Flip the tree” and determine the probability that given it’s an acceptable capacitor it is manufactured by machine M1. (c) Find (i) P(M1 | not A) (ii) P(M2 | A) (iii) P(M2 | not A). You may wish to use Bayes’ Theorem to check your answers.
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.
8. Capacitors are made by 2 machines, M1 and M2. The probability that a capacitor is manufactured acceptably varies according to the machine. The probabilities are 0.9 and 0.95 respectively for machine M1 and M2. Machine M1 manufactures 80% of the capacitors.
(a) Draw a tree diagram and attach the probabilities for every branch and outcome.
(b) “Flip the tree” and determine the probability that given it’s an acceptable capacitor it is manufactured by machine M1.
(c) Find
(i) P(M1 | not A)
(ii) P(M2 | A)
(iii) P(M2 | not A).
You may wish to use Bayes’ Theorem to check your answers.
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