Mrs Reena has regularly contacted three companies (A, B and C) for her quarterly servicing of aircons. If A services her aircons, the probability that there will be no problem with the aircons in the next quarter is 0.8. The same probability for B is 0.7 and for C is 0.6. If all her aircons do not show any problems, she will engage the same company in the next quarter. If any of the aircons shows a problem, then she will engage A with a probability of 0.5, B with a probability of 0.3 or C with a probability of 0.2 in the next quarter. One of her aircons had a problem last quarter. (i) Identify the probability that her aircons will have no problem in the next quarter.
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.
Mrs Reena has regularly contacted three companies (A, B and C) for her quarterly
servicing of aircons. If A services her aircons, the
no problem with the aircons in the next quarter is 0.8. The same probability for B
is 0.7 and for C is 0.6. If all her aircons do not show any problems, she will engage
the same company in the next quarter. If any of the aircons shows a problem, then
she will engage A with a probability of 0.5, B with a probability of 0.3 or C with
a probability of 0.2 in the next quarter. One of her aircons had a problem last
quarter.
(i) Identify the probability that her aircons will have no problem in the next
quarter.
(ii) Given that her aircons had no problem in the next quarter, what is the
probability that she engaged C?
(iii) What is the probability that she will engage A for the next two quarters?
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