Name /or ID Question 11. (WARRANTY MAY HELP An electric bulb making company offe

Question

Name /or ID Question 11. (WARRANTY MAY HELP An electric bulb making company offers two warranty periods at two different costs. The first warranty offer is for 2 years, and the second warranty offer is for five years. No doubt the five year warranty period is more expensive the two year warranty period. The probability that a bulb can burn out in the first two years is 0.1+ DGC DGC + 500 = and in the third to fifth year is Giant light bulbs 0.15 given that does not burn out in the first two years of warranty. Bob buys a packet of seven light bulbs. (I) In the two year warranty period, what is the probability that x bulbs will burn out? (a ) What is the probability that none of the bulbs will burn out during the warranty period of two years? (b) What is the probability that more than one of the bulbs will burn out during the warranty period of two years?

Explanation / Answer

Solution

First 2 years probability of bulb burn out = 0.1 + 441/941 = 0.569

1) P(X=x) = 7Cx (0.569)x (0.431)7-x

(a) P(none of the bulb will burn out) = P(X=0)

= 7C0 (0.569)0 (0.431)7-0 = 0.0028

(b) P(X>1) = 1-P(X<=1) = 1- (P(X=0)+P(X=1))

= 1- (0.0028 + 7C1 (0.569)1 (0.431)6)

= 0.972

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