Need help with this problem s als ndep ndent Traffic engine

Need help with this problem:

s als ndep ndent . Traffic engineers install 14 street lights with new bulbs. The probability that a bulb wil ail within 50000 hours of operation s (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? 2·Assu m that each o the (a Your answer should be correct to 3 decimal places. Your answer should be correct to 3 decimal places. Your answer should be correct to 6 decimal places. (o)l

Solution

Ans a)

Pr(x<=1)=14C0(0.21)^0*(0.79)^14)+14C1(0.29)^1(0.71)^13=0.79^14+14(0.21)*(0.79)^13=0.79^13(0.79+14(0.21))=0.174

Ans b)

Pr(x=0)=14C0(0.21)^0*(0.79)^14)=0.79^14=0.0368

Ans c)

Pr(x>4)=1-Pr(x<4)

Pr (x<4)=14C0(0.21)^0*(0.79)^14)+14C1(0.21)^1(0.79)^13+14C2(0.21)^2(0,79^12)+14C3(0.21)^3(0.79)^11+14C4(0.21)^4(0.79)^10)

=0.174+91*(0.21^2)(0.79^12)+364(0.21^3)(0.79)^11+1001(0.21^4)(0.79)^10=0.663

Pr(x<4)=0.847

Pr(x>4)=1-0.847=0.153