Traffic engineers install 12 street lights with new bulbs. the probability that a bulb will fail within 50000 hours of operation is 0.26. 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 will need replacing within 50000 hours?

Question

Joe Kent

Mathematics

23 November, 18:32

Traffic engineers install 12 street lights with new bulbs. the probability that a bulb will fail within 50000 hours of operation is 0.26. 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 will need replacing within 50000 hours?

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Karsyn Soto · Answer 1

(a) The probability that 0 or 1 bulbs will fail is given by a suitable probabiity calculator as 0.14065.

(b) The probability that 0 bulbs will fail is given by a suitable probability calculator as 0.02696.

This is the probability that all bulbs will remain good: (1 - 0.26) ^12.

(c) The probability that 5 or more bulbs will fail is the complement of the probability that 4 or fewer will fail. A suitable probability calculator shows the desired probability to be 0.17897.