The rooftop bar of a fancy hotel can only be accessed via the two hotel elevators. If one of the elevators is out of order, long queues will form in front of the remaining elevator and customers complain to the bar manager. This is why they know from their experience that the probability that Elevator A works but Elevator B is out of order is 3%, while the probability that Elevator B works but Elevator A is out of order is 4%. Assuming that both elevators function independently of each other, what is the probability that the rooftop bar has to close because both elevators are out of order? To answer this question, proceed as follows: (a) Let p be the probability that both elevators are out of order. Show that p satisfies the quadratic equation p^2 − 0.93p + 0.0012 = 0. (b) Solve this equation and explain which of the two solutions gives the correct value for p.
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.
The rooftop bar of a fancy hotel can only be accessed via the two hotel elevators. If one of the elevators is out of order, long queues will form in front of the remaining elevator and customers complain to the bar manager. This is why they know from their experience that the probability
that Elevator A works but Elevator B is out of order is 3%, while the probability that Elevator B works but Elevator A is out of order is 4%.
Assuming that both elevators
(a) Let p be the probability that both elevators are out of order. Show that p satisfies the
p^2 − 0.93p + 0.0012 = 0.
(b) Solve this equation and explain which of the two solutions gives the correct value for p.
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