In a string of 100 Christmas lights there is a 014 chance th

In a string of 100 Christmas lights, there is a .014 chance that a given bulb will fail within the first year of use (if one bulb fails, it does not affect the others).

Find the approximate probability that five or more bulbs will fail within the first year. (Round your answer to 4 decimal places.)

Solution

It can also be calculated by substracting the probability that less than 5 will fail,

P=1-(P<5 will fail)

=P(o fail)+p(1fail)+P(2 fail)+P(3fail)+P(4 fail)

Probability of not fail=0.986

Ans = 100C0 *(0.986)^100 +100C1*(0.014)*(0.986)^99+100C2*(0.014)^2*(0.986)^98+100C3*(0.014)^3*(0.986)^97+100C4*(0.014)^4*(0.986)^96

Calculate and this will be the answer