SOLUTION: A power station has two generators, each failing with probability of 5% in a year, independently from one year to the next. Assuming failure of a generator is independent of each o

Algebra.Com
Question 776277: A power station has two generators, each failing with probability of 5% in a year, independently from one year to the next. Assuming failure of a generator is independent of each other and between each year, what is the probability of both generators failing in the same year at least once in a ten year period?
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
A power station has two generators, each failing with probability of 5% in a year, independently from one year to the next. Assuming failure of a generator is independent of each other and between each year, what is the probability of both generators failing in the same year at least once in a ten year period?
-----------
P(both fail in one year) = 0.05^2 = 0.0025
-----------
Binomial Problem with n = 10 and p(both fail) = 0.0025
-----------
P(1<= x <=10) = 1-P(x=0) = 1 - 0.9975^10 = 0.0247
=====================================================
Cheers,
Stan H.
===========

RELATED QUESTIONS

A school has two bacup generators having probabilitiesof 0.9 and respectively , of... (answered by solver91311)
: A school has two backup generators having probabilities of 0.9 and 0.95, respectively , (answered by stanbon)
Q1. You deposit $3,000 in a savings account that earn 9% simple interest per year. How... (answered by ikleyn)
Q1. You deposit $3,000 in a savings account that earn 9% simple interest per year. How... (answered by ikleyn)
Shell has recently signed a sale and purchase agreement (SPA) with XTRA Pty Ltd. to... (answered by ikleyn)
Rational Word Problem: A generator in an electrical power produces 10 MW (megawatts) of... (answered by ikleyn)
Below is a probability distribution showing the year after purchase in which a certain... (answered by stanbon)
The number of sick days an employee takes in one year is uniformly distributed on the... (answered by math_tutor2020)
How strange are coincidences? Suppose an event has a 1 in 500 chance of happening each... (answered by ikleyn,robertb)