Question

there are four copy machines in the library. it is estimated that the probability that a particular copy machine is out of order is 0.3. assuming that the machines work independently of each other what is the probability that at least one machine is out of order the next time you go to the library?

Answer 1

≅ 0.76 or 76%

Explanation:

To find the probability that at least one copy machine is out of order, we can use the complement rule. That is, we can find the probability that none of the copy machines are out of order, and then subtract that from 1.

The probability that a particular copy machine is working is 1 - 0.3 = 0.7. Since we have four copy machines that work independently of each other, the probability that all four machines are working is:

0.7 x 0.7 x 0.7 x 0.7 = 0.2401

So the probability that none of the copy machines are out of order is 0.2401.

Therefore, the probability that at least one machine is out of order is:

1 - 0.2401 = 0.7599

So the probability that at least one copy machine is out of order is approximately [0.76, or 76%.]