Problem 213SE

It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that now has a total of 75 copies of the program. A sample of copies will be selected from the lot without replacement.

(a) If three copies of the software are inspected, determine the probability that exactly one of the defective copies will be found.

(b) If three copies of the software are inspected, determine the probability that both defective copies will be found.

(c) If 73 copies are inspected, determine the probability that both copies will be found. (Hint: Work with the copies that remain in the lot.)

Answer

Step 1 of 3

(a)

It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that now has a total of copies of the program.

A sample of copies will be selected from the lot without replacement.

we are asked to find the probability that exactly one of the defective copies will be found if three copies of the software are inspected.

Let denote the defective copy of the software.

Let denote the original copy of software or without defect

The number of ways we can inspect exactly one defects from the three copies of the software is using combination theorem since the sample of copies are selected from the lot without replacement.

We can write our sample space of exactly one defects,

……..(1)

The probability of defective copies from the shipping lot that has a total of copies is,

The probability that exactly one of the defective copies is using equation (1)

Hence the probability that exactly one of the defective copies will be found is