Traffic engineers install 12 street lights with new bulbs. The probability that

Question

Traffic engineers install 12 street lights with new bulbs. The probability that a bulb will fail within 50000 hours of operation is 0.29. Assume that each of the bulbs fails independently. (a) What is the probability that fewer than two of the original bulbs will fail within 50000 hours of operation? (b) What is the probability that no bulbs will have to be replaced within 50000 hours of operation? (c) What is the probability that more than four of the original bulbs wll need replacing within 50000 hours? (a)|........urYour answer should be correct to 3 decimal places. (b)l0.016 Your answer should be correct to 3 decimal places. rx Your answer should be correct to 6 decimal places.

Explanation / Answer

Given that the probabilityof bulb tht it will fall within 50000 hrs of operation= 0.29

Hnece The probability of Bulb which replaced within 50000 hrs is 1-0.29 =0.71

Hence Accordimg to question

a) Probability of less than 2 bulb fall within 50000 hrs of operation hence out of 12 bulbs 10 balls replaced within the 50000 hrs

Hence, P= 12C1*P( Within 50k hrs)n *P ( Replaced within 50k hrs)x-n

so, = 12* (0.29)1(0.71)11

= 0.080

And similarly for probability for no bulb within operation calculated as

= 0.016 hence

Probability for fewer to 2 is 0.016+0.080

=0.097

Similarly

b) Probability for no ball alls within 50k hrs of operation

P= 12C0*P( Within 50k hrs)n *P ( Replaced within 50k hrs)x-n

= 1* (0.29)0*(0.71)12 = 0.016

c) Similary Probabiility of more than 4 bulbs will need replacing since probability of replacing is 0.71

P(More than 4 bulbs to be replaced) calculated as

= 0.992414

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