Question

A burglar alarm system has six fail-safe components. the probability of each failing is 0.05. find the probability that exactly three will fail. round to the nearest thousandth.

Answer 1

0.002 For 6 systems with exactly 3 failures, you need to calculate 6 pick 3 or 6!/(3!3!) = 720/(6*6)=720/36=20 different combinations of 3 systems to fail. Now the probability of each of those failures will be the probability of the subsystems not failing times the probability of the subsystems fail. So 0.95^3 * 0.05^3 for 3 subsystem not failing time 3 subsystems failing. So 0.95^3 * 0.05^3 = 0.857375*0.000125 = 0.000107172. And multiply by the 6 pick 3 calculated earlier, gives. 0.000107172 * 20 = 0.002143438 And rounding to the nearest thousandth, gives 0.002