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Actually, I don't know if the first answer is correct.

The problem states:

"The probability that ONLY the older pump will fail is 0.10, and the probability that ONLY the newer pump will fail is 0.05".

This means that the probability of the older pump failing is 0.1 + the probability that they both fail: P(A Intersect B).

The same goes for the newer pump.

So P(Older Pump) = 0.1 + x

and P(Newer Pump) = 0.05 + x

The P(They both fail) = P(Older Intersect Newer)

= (0.1 + x)*(0.05 + x) - x

= x^2 - 0.85x + 0.005 (a quadratic equation)

Find the roots of the equation and use the smaller one: 0.0059

This answer is incorrect. The question states probs that ONLY a particular pump fails, not the prob that the pump fails.

The answer completely disregards the fact that "only" the older pump will fail and "only" the newer pump will fail.

I can teach and explain topics up to Differential Equations. Although Statistics has always been my weakest subject, I am very capable in Combinatorics and Probability.

38 years of teaching college-level math, mostly at a two-year college.**Publications**

Journal of Recreational Mathematics.
In the mid-1980's I had a bi-montly column in BYTE magazine, combining recreational math and programming in BASIC.**Education/Credentials**

BS and MS in mathematics, SUNY Albany