Question

Problem 2.213 It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that has now a total of 7 your answers to five decimal places (e.g. 98.76543). 0 copies of the program. A sample of coples will be selected e copies of the software are inspected, determine the probability that exactly one of the defective copies will be found (b) If three coples of the software are inspected, determine the probability that both defective copies will be found (c) If 68 copies are inspected, determine the probability that both copies will be found. (Hint: Work with the copies that remain in the lot. Statistical Tables and Charts

Answer 1

Out of 70 copies 2 are defective and rest 68 are good copies.

(a)

Among the 3 copies, 1 copy is selected from the 2 defective copies and rest 2 copies are selected from the 68 good copies. So, the number of ways this can be done = 2C1 * 68C2 = 4556. And no of ways, 3 copies can be selected from 70 copies = 70C3 = 54740

Desired probability = 4556 / 54740 = 0.08323

(b)

Similarly as above, desired probability = (2C2 * 68C1) / 70C2 = 0.02816

(c)

Desired probability = (2C2 * 68C66) / (70C68) = 0.94327

** If these answers do not match please comment.