A store shelf contains 100 light bulbs but 4 are defective Y

A store shelf contains 100 light bulbs, but 4 are defective. You buy six of them. (show work)

A. What is the probability you get all four defective bulbs?

B. What is the probability you get no defective bulbs?

C. What is the probability you get two defective bulbs?

D. What is the probability you get at least one defective bulb?

Solution

There are 100C4 = 3921225 ways buy 4.

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A.

There\'s only 1 way to get all 4 wrong.

Thus, the probability is 1/3921225 = 0.000000255022 [answer]

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B.

There are 96C4 = 3321960 ways to get no defective bulbs.

Thus,

P = 3321960/3921225 = 0.847174034 [answer]

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C.

There are (96C2)(4C2) = 27360 ways to do this.

Thus,

P = 27360/3921225 = 0.006977411 [answer]

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D.

As

P(at least one defective) = 1 - P(no defective),

P(at least one defective) = 1 - 0.847174034

= 0.152825966 [ANSWER]