BastiG wrote:
Can someone pls explain why (0.05)*(0.95^13)) is multiplied with (14).
14*(0.05)*(0.95^13) represents the probability that
exactly one of the machines breaks down. You could first ask - what's the probability the first machine breaks down, and the other thirteen machines work? This would be equal to
(0.05)*(0.95)*(0.95)*...*(0.95) = (0.05)*(0.95^13)
Now, if we find the probability the second machine breaks down and the others work, this will be equal to
(0.95)*(0.05)*(0.95)*(0.95)*...*(0.95) = (0.05)*(0.95^13)
Similarly, the probability the third machine will be the only one that breaks down will be (0.05)*(0.95^13), and so on. We'll get 14 individual probabilities like this. To find the probability that
any one machine breaks down, we'd add the probability that only the first breaks down, the probability that only the second breaks down, the probability that only the third breaks down, etc, so we'd get 14*(0.05)(0.95^13).
That's the long explanation, just to explain why this faster method works: you can first find the probability that one machine fails in some specific sequence: (0.05)(0.95^13). You can then multiply this by the number of sequences in which exactly one machine fails: 14.
I'd add that this type of probability question is only very rarely asked on the GMAT, and it is *far* more important to become comfortable with the more basic concepts of probability. If you are comfortable with the more elementary types of probability questions, you might, however, try to apply the above to a question like the following, which has numbers more like what you'd see on the GMAT:
In a certain city, the probability of rain on any given day is 0.7. What is the probability it rains on exactly one day in a certain five day period?
