The probability that coal fired electric generator 1 is working is .10. The probability that coal fired electric generator 2 is working is .20. What are the probabilities that: Both work? Neither work? Only one works?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
HINTS: Assuming that the generators are completely independent, the probability that both work is the product of the individual probabilities of their working, or $0.10\cdot0.20=0.02$. (Without that some assumption about dependence or independence of the generators the questions cannot be answered; unless the point of the question is to see whether you understand that this information is necessary, you’re probably expected to assume independence of the generators, and I will do so.)
The probability that the first generator does not work is $1.00-0.10=0.90$. What is the probability that the second generator does not work? What is the probability that both fail to work? This problem is now just like the first one.
If you’ve got this far, you know the probability that both work and the probability that both fail to work. The event that exactly one of them works covers all other outcomes, and the probabilities of the possible outcomes must add up to $1$, so the probability that exactly one works is ... ?
My 8th grader writes thusly:
"Even though there is not enough information provided, Assuming that there are no dependencies: $(1/10)*(2/10) = (2/100)$ so the probability of them both working is 2 out of 100. $(9/10)*(8/10) = (72/100)$ so the probability of neither working is 72 out of 100, or 36 out of 50, or 18 out of 25. $(1/10)*(8/10) = (8/100)$ and $(9/10)*(2/10) = 18/100$ so the final product should be $(8/100)+(18/100)=(26/100)$"
(Please do not upvote or downvote; it was his work. If inappropriate, I will delete.)
Hint: The chance that a given one is not working is 1 minus the chance that it is working. If you assume that the events of each working are independent, the probability they both work is the product of the probability of each.