using TI-84 plus... Traffic engineers install 5 street lights with new bulbs. Th

Question

using TI-84 plus...

Traffic engineers install 5 street lights with new bulbs. The probability that a bulb will fail within 50020 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 50020 hours of operation?
(b) What is the probability that no bulbs will have to be replaced within 50020 hours of operation?
(c) What is the probability that more than four of the original bulbs will need replacing within 50020 hours?

Explanation / Answer

here p = 0.26

(A)

P(X<2) = P(X=0) + P(X=1)

=5C0*p^0*(1-p)^5 + 5C1*p^1*(1-p)^4

= 0.6117

(B)

P(X=0) = 5C0*p^0*(1-p)^5

= 0.2219

(C)

P(X>=4) = P(X=4) + P(X=5)

= 5C4*p^4*(1-p)^1 + 5C5*p^5*(1-p)^0

= 0.0181

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