Ten light bulbs are tested to see if they last as long as the manufacturer claim

Question

Ten light bulbs are tested to see if they last as long as the manufacturer claims they do. Of these 1 three light bulbs were defective (ailed the test). Two light bulbs are selected at random (from the tweive) without replacement. a) Find the probability that both light bulbs selected are defective. b) Find the probability that both light bulbs selected are not defective. c) Find the probability that at least one light bulb is defective. 7. A college has an undergraduate enrollment of 3600. Of these, 860 are business majors and 1800 are women. Of the business majors, 424 are women. a) If a student is selected at random, what is the probability that the selected student is a woman or a business major? b) If a student is selected at random, what is the probability that the selected student in not a business major? c) If a student is selected om buS a male student?

Explanation / Answer

6)

a) probability that both bulb are defective =P(first one defective& second onde defective)=(3/10)*(2/9)=0.0667

b)probability that both bulb are non-defective =P(first one non-defective& second one non-defective)=

=(7/10)*(6/9)=0.4667

c)probability that at least one is defective =1-P(both are non-defective)=1-0.4667=1-0.5333

7)

for above information we can prepare below table:

a) probability that selected student is women or business major =(424+1376+436)/3600= 0.6211

b) probability that selected student in not a business major =2740/3600=0.7611

c)probability of male student given business najors =436/860=0.5070

please revert for any clarification

business major non-business major total women 424 1376 1800 men 436 1364 1800 total 860 2740 3600

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