5. A shipment of 50 light bulbs contains 10 defective light bulbs. In order to test...

5. A shipment of 50 light bulbs contains 10 defective light bulbs. In order to test the quality of the shipment, a quality control engineer selects 5 light bulbs at random.

(a) How many different samples are possible?
(b) What is the probability the engineer will select exactly two defective light bulbs?

(c) The shipment will be rejected if at least one of the light bulbs in the sample is defective. What is the probability the sample will be rejected?

in part b and c. plz, using another way to solve it. except for binomial distribution.

Solutions

Expert Solution

a) The total number of different samples possible here is computed as:
= Number of ways to select 5 light bulbs from 50 light bulbs

Therefore there are 2118760 different samples possible here.

b) The probability that the engineer will select exactly two defective light bulbs is computed here as:
= Number of ways to select 2 defective ones from 10 defective ones * Number of ways to select 3 non defective ones from remaining 40 light bulbs / Total ways to select 5 bulbs from 50 bulbs

Therefore 0.2098 is the required probability here.

c) The probability that the shipment is rejected is computed here as:

= 1 - Probability that none of the 5 selected ones are defected

= 1 - (Number of ways to select 5 bulbs from 40 non defective ones) / Total ways to select 5 bulbs from 50 bulbs

Therefore 0.6894 is the required probability here.

orchestra answered 1 year ago

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