A city uses three pumps to carry water from a river to a reservoir. Pumps A and B are new, and have a probability of failing of 0.015 on any day. Pump C is older, and has a probability of failure of 0.08 on any day. Pumps A and B operate Monday-Friday. On Saturday, pumps A and C operate while pump B is serviced. On Sunday, pumps B and C operate while pump A is serviced. Answer the following questions, assuming that the pumps operate independently of one another, and independently from day to day. Determine the probability that pump A works on a day that it is in use. Find the probability that pumps A and B both fail on a day they are both in use. Compute the probability that at least one pump fails on any Sunday.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.