If a watch has a 0.12 defect rate. what is the probability that the watch has fewer than 3 defects in a run of 75 chimes?

Step-by-step explanation:

If a watch has fewer than three defects, then either 1.) It has no defects, 2.) it has exactly 1 defect, or 3.) it has exactly 2 defects.

1.) The probability that the watch has no defects is , because for every chime there is a probability of that there is no defect

2.) The probability that the watch has exactly 1 defect is times the number of ways you can choose 1 of 75 of the chimes to be defective, which is , so the probability that the watch has exactly 1 defect is .

3.) For the same reason as 2.), the probability that the watch has exactly two defects is

Since 1.), 2.), and 3.) are mutually exclusive events, the probability of their union is simply the probability of each of them added together, which is

she will travel a distance in the range of 3 - 11 miles