Question

Next Question A company was founded in California to provide electronic devices and computer pro of 23 processors was sent to the company. Eight of them were defective. One of the company's statisticians selected 5 of the processors to put in his parts inventory, and went on three service calls. Complete parts a and b below. a. Determine the probability that only 1 of the 5 processors is defective. Klavye The probability is (Round to five decimal places as needed.) b. Determine the probability that 3 of the 5 processors are not defective. The probability is (Round to five decimal places as needed.)

Answer 1

a. 0.32453

b. 0.82526.

Step-by-step explanation:

a. The probability that only one processor is defective out of the five selected by the statistician is equal to the number of ways of selecting one defective processor out of the total 8 defective processors multiplied by the number of ways of selecting 4 good processors out of the 15 good processors, divided by the total number of ways of selecting 5 processors out of the total 23 processors.

Here the defective processors are all identical and the working processors are all identical. So we use the combinations in stead of permutations.

probability = 8C1 * 15C4 / 23C5

or 5 * 8/23 * 15/22 * 14/21 * 13/20 * 12/19

= 0.32453

b. Probability that 3 of the 5 processors selected are not defective

= 1 - probability that 3 of the 5 processors selected are defective

= 1 - 8C3 * 15C2 / 23C5

= 1 - 0.17474 = 0.82526.

or, the probability

= 1 - 5C3 * 8/23 * 7/22 * 6/21 * 15/20 * 14/19 = 1 - 0.17474

= 0.82526.