SOLUTION: 5% of the parts produced in a manufacturing process are defective. Each part is tested for defects. If the part is defective, the test will indicate it is defective 98% of the time

Question 842153: 5% of the parts produced in a manufacturing process are defective. Each part is tested for defects. If the part is defective, the test will indicate it is defective 98% of the time. If the part is not defective, the test will indicate it is defective 1% of the time.
What is the probability that a randomly selected part from this population tests defective?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
5% of the parts are defective.
if the part is defective, the test will indicate that it is defective 98% of the time.
if the part is not defective,l the test will indicate that it is defective 1% of the time.

you select a part from the from the population.

5% of the time it is defective, so 98% of 5% of the time you will test it to be defective. 5% of 98% is equal to .05 * .98 which is equal to .049 which is equal to 4.9% of the time.

95% of the time it is not defective, so 1% of 95% of the time you will test it to be defective. 1% of 95% is equal to .01 * .95 which is equal to .0095 which is equal to .95% of the time.

since the total percent of the time is equal to 5% plus 95%, the total percents of the time a randomly selected part will test defective will be 4.9% + .95% which is equal to 5.85% of the time.

a randomly selected part will test defective 5.85% of the time.

let's see how this works in the real world.

let's assume your population consists of 5000 defective parts and 95000 parts that are not defective.

let's assume you test them all.

you will test 5000 defective parts and 98% of the time you will test them as defective so you will conclude that .98 * 5000 = 4900 of them are defective.

you will test 95000 good parts and 1% of the time you will test them as defective so you will conclude that .01 * 95000 = 950 of them are defective.

the total number that you concluded were defective is 4900 + 950 = 5850.

take 5850 and divide it by 100,000 and you get .0585 which means that you will have concluded that 5.85% of the parts are defective, even though only 5% were actually defective.

the numbers check out so i'm reasonably confident that the solution is good.

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