Flammable gas-leaks can be disastrous for power plants. To prevent disasters, gas-sensors are placed at strategic locations. These sensors are periodically tested for their accuracy. At a factory, 64 of these sensors are installed. 12 sensors are checked weekly, and the complete set is replaced if at least one defective sensor is found. (a) If 12 of the sensors in the set are defective, what is the probability that the set is replaced the first day it is evaluated? (b) If 12 of the sensors in the set are defective, what is the probability that the set is not replaced until the third day of evaluation? (c) Suppose on the first day of evaluation, two of the sensors are defective, on the second day of evaluation six are defective, and on the third day of evaluation, ten are defective. What is the probability that the set is not replaced until the third day
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.
Flammable gas-leaks can be disastrous for power plants. To prevent disasters, gas-sensors are placed at strategic locations. These sensors are periodically tested for their accuracy. At a factory, 64 of these sensors are installed. 12 sensors are checked weekly, and the complete set is replaced if at least one defective sensor is found.
(a) If 12 of the sensors in the set are defective, what is the
(b) If 12 of the sensors in the set are defective, what is the probability that the set is not replaced until the third day of evaluation?
(c) Suppose on the first day of evaluation, two of the sensors are defective, on the second day of evaluation six are defective, and on the third day of evaluation, ten are defective. What is the probability that the set is not replaced until the third day
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