Question

Eight percent, 8%, of Christmas tree light bulbs manufactured by a company are defective. bulbs are randomly taken and inspected one at a time. 1. What is the probability that the first defective bulb was the 7th bulb that was inspected? 2. What is the probability that the third defective bulb was the 7th bulb that was inspected?

          Eight percent, 8%, of Christmas tree light bulbs manufactured by a company are defective. bulbs are randomly taken and inspected one at a time.
1. What is the probability that the first defective bulb was the 7th bulb that was inspected? 
2. What is the probability that the third defective bulb was the 7th bulb that was inspected?
        
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Eight percent, 8%, of Christmas tree light bulbs manufactured by a company are defective. bulbs are randomly taken and inspected one at a time. 1. What is the probability that the first defective bulb was the 7th bulb that was inspected? 2. What is the probability that the third defective bulb was the 7th bulb that was inspected?
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Transcript

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00:01 So in this question we had given probability of defect p is equal to 1 % which is equal to 0 .01 and probability of not of not defect probability of and probability of not defect and probability of not defect q is equal to 1 minus p which is equal to 0 .99.
00:38 Now we know that for this distribution probability of d equal to k is equal to n ck multiply by p to the power k multiply by q to the power n minus k so this is the formula for this is the formula for distribution now for the a part for the a part probability of defects is equal to probability of defects is equal to pd equal to 2 which is equal to 8 c2 multiply by 0 .01 square multiply by 0 .998 minus 2 which is equal to 28 multiplied by 0 .01 square multiplied by 0 .99 to the power 6 which is equal to 0 .0026 which is equal to 0 .0026.
02:06 So this is the answer for a part.
02:10 Now for the b part, probability of money back is equal to probability of d greater than 1.
02:28 So probability of d greater than 1 is equal to 1 minus probability of d equal to 0 plus p d equal to 0.
02:41 To 1.
02:43 So here we get it as 1 minus 8 c0 multiply by 0 .01 to the power 0 multiply by 0 .99 to the power 8 minus 0 plus 8c1 multiply by 0 .01 1 x0 .1 multiply by 0 .99 to the power 8 minus 1...
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