A Southwest Energy Company pipeline has 3 safety shutoff valves in case the line springs a leak. These valves are designed to operate independently of one another. There is only a 7% chance that valve 1 will fail at any one time, a 10% failure chance for valve 2, and a 5% failure chance for valve 3. If there is a leak, find the following probabilities: that at least one valve operates correctly.
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 Southwest Energy Company pipeline has 3 safety shutoff valves in case the line springs a leak. These valves are designed to operate independently of one another. There is only a 7% chance that valve 1 will fail at any one time, a 10% failure chance for valve 2, and a 5% failure chance for valve 3. If there is a leak, find the following probabilities:
- that at least one valve operates correctly.
Given that there is a 7% chance that valve 1 will fail, a 10% chance that valve 2 will fail, and a 5% chance that valve 3 will fail.
That is,
Probability that valve 1 will fail is 0.07.
Probability that valve 2 will fail is 0.10.
Probability that valve 3 will fail is 0.05.
Given that all the 3 valves works independently.
The probability that all the 3 valves will fail is calculated as follows:
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