Traffic engineers install 6 street lights with new bulbs. The probability that a

Question

Traffic engineers install 6 street lights with new bulbs. The probability that a bulb will fail within 50040 hours of operation is 0.23. Assume that each of the bulbs fails independently.
(a) What is the probability that fewer than two of the original bulbs will fail within 50040 hours of operation?
(b) What is the probability that no bulbs will have to be replaced within 50040 hours of operation?
(c) What is the probability that more than four of the original bulbs will need replacing within 50040 hours?

Explanation / Answer

a) x can assume 0 or 1 n=12 nCx * p^x * q^(n-x) 12C0 * (0.26)^0 * (0.74)^12 = 0.027 12C1*(0.26)^1 * (0.74)^11 =0.112 so the total probability for question (a) is 0.027+0.112 = 0.139 b) 0.027 as derived for question (a) c) as we calculated for (a) we know the probability for 0 and 1 similarly calculate for 2,3 and 4 total the answer and add it with answer derived in (a) get the value subtract it from 1 and that,s the answer

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