A carton of light bulbs contains ten 40-watt bulbs and twelve60-watt bulbs. Eigh

Question

A carton of light bulbs contains ten 40-watt bulbs and twelve60-watt bulbs. Eight of the light bulbs are defective. a) What is the probability that exactlty half of the defectivebulbs are 40-watt bulbs? b) What is the probability that at most two of the defectivebulbs are 60-watt bulbs? A carton of light bulbs contains ten 40-watt bulbs and twelve60-watt bulbs. Eight of the light bulbs are defective. a) What is the probability that exactlty half of the defectivebulbs are 40-watt bulbs? b) What is the probability that at most two of the defectivebulbs are 60-watt bulbs?

Explanation / Answer

i)      =>4 defective bulbs are40W and rest 4 are 60 W =>toatal probability of having 8 defective bulbs is8Cr 10^r 12^(8-r) = (10+12)^8 = 22^8 prob dat exact 4 40 W are defective = 8C4 (10^4)(12^4) =70*(10^4)(12^4) hence the required exact probability is [70(10^4)(12^4)] / [22^8] ii) =>total probability remains same here probability dat at most two of the defective bulbs are 60W                            = 8C6 (10^6)(12^2) + 8C7(10^7)(12^1) +8C8 (10^8)(12^0)               so the required probability is          [8C6 (10^6)(12^2) + 8C7(10^7)(12^1) +8C8 (10^8)(12^0)] / [22^8 ]

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