UTILITIES A city water system includes a sequence of 4 pumps...

UTILITIES A city water system includes a sequence of 4 pumps as shown below. Water enters the system at point $A,$ is pumped through the system by pumps at locations $1,2,3,$ and $4,$ and exits the system at point $B .$ If the probability of failure for any one pump is $\frac{1}{100},$ what is the probability that water will flow all the way through the system from A to $\mathrm{B} ?$

UTILITIES A city water system includes a sequence of 4 pumps as shown below. Water enters the system at point $A,$ is pumped through the system by pumps at locations $1,2,3,$ and $4,$ and exits the system at point $B .$
If the probability of failure for any one pump is $\frac{1}{100},$ what is the probability that water will flow all the way through the system from A to $\mathrm{B} ?$

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Key Concepts

Independent Events

This concept involves events whose outcomes do not affect one another. In probability, when events are independent, the result of one does not influence the result of the others, allowing us to calculate the probability of multiple events occurring by treating each event separately.

Multiplication Rule of Probability

The multiplication rule states that if events are independent, the overall probability of all events occurring is the product of their individual probabilities. This rule is crucial when evaluating the probability of a sequence of independent events all taking place.

Series System Reliability

In a series system, the overall system functions only if every individual component functions. The reliability of such a system is determined by multiplying the reliability (probability of success) of each component. This concept is widely used in engineering and reliability analysis to assess the performance of systems where one component's failure results in the failure of the entire system.

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