Question

Suppose you have 31 formatted computer disks of which 5 are defective. For a particular backup procedure you will pick 3 disks at random. What is the likelihood that only one good or acceptable disk will be picked?

57.8%
36.2%
16.1%
83.9%
5.8%
0.22%
​

Answer 1

To find the probability of only one good or acceptable disk being picked out of 3 disks, consider two scenarios: picking 2 defective disks and 1 good disk, and picking 2 good disks and 1 defective disk. Calculate the probabilities for each scenario using the combination formula and multiply them together to get the overall probability.

Step-by-step explanation:

To find the probability of only one good or acceptable disk being picked out of 3 disks, we need to consider two scenarios: 1) picking 2 defective disks and 1 good disk, and 2) picking 2 good disks and 1 defective disk.

Scenario 1: The probability of picking 2 defective disks out of the 5 defective disks can be calculated using the combination formula. The probability of picking 1 good disk out of the remaining 26 acceptable disks can also be calculated using the combination formula. Multiply these probabilities together to get the probability of scenario 1.

Scenario 2: The probability of picking 2 good disks out of the remaining 26 acceptable disks can be calculated using the combination formula. The probability of picking 1 defective disk out of the 5 defective disks can also be calculated using the combination formula. Multiply these probabilities together to get the probability of scenario 2.

Add the probabilities of scenario 1 and scenario 2 to get the overall probability of only one good or acceptable disk being picked.