Pls help!

The probability that a processor fails before operating 1000 hours is 1/5. Determine the probability that among 6 processors, at least 2 will fail before operating 1000 hours.

Question

Pls help!

The probability that a processor fails before operating 1000 hours is 1/5. Determine the probability that among 6 processors, at least 2 will fail before operating 1000 hours.

anonymous · Answer

Well the chance for one processor to fail is 1/5. But you want to know when at least TWO fail. So whats the probability of both failing? (1/5) X (1/5) = (1/25). So the answer is 1/25.

kropot72 · Answer

The number of combinations of 6 processors taken two at a time is 6C2 = 15
The probability of each pair failing is$$\frac{1}{5}\times \frac{1}{5}=\frac{1}{25}$$
Therefore the probability of at least 2 failing before 1000 hours is
$$15\times \frac{1}{25}=\frac{3}{5}$$

anonymous · Answer

Thanks to you all, kropot72 and nolastudent! Please which solution is correct? I sincerely appreciated your efforts.

kropot72 · Answer

Why not bump your question to the top to see if people with high Smart Scores give medals or comments?

anonymous · Answer

ok kropot72. I will do so. Thanks!

kropot72 · Answer

@vic1 The probability of just one pair of processors failing is 1/5 * 1/5 = 1/25. But there are 15 combinations of pairs among the 6 processors, so to include all these 15 possible pairs we must multiply 1/25 by 15 = 15/25

kropot72 · Answer

@vic1 Your reply to @emcrazy belongs elsewhere :)

anonymous · Answer

You are looking for an event where at least two fail. The probability of ONE failing is 1/5. Now you want another one to fail, so the probability for the second processor is 1/5 (on its own). You are looking for at LEAST two failures, so after two failures, you don't need to worry about the other processors failing or surviving, so the probability of each of the remaining processor to either fail or survive is 1/1 = 1 (because it doesn't matter if more than two processors fail). So lets multiply the probabilities to get the total probabilities: first the two failed ones and then the four ones we don't care about: (1/5) x (1/5) x 1 x 1 x 1 x 1 = (1/25). @kropot72 , You can do a combination with selecting two out of six because the problem says at LEAST two, so three, four, five, or all six processors failing is okay.