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In a string of 100 christmas lights, there is
a.015 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 six or more bulbs will fail within the first year. (round your answer to 4 decimal places.) probability

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LammettHash
We want to find [tex]\mathbb P(X\ge6)[/tex], where [tex]X[/tex] is a binomial distribution with [tex]n=100[/tex] and [tex]p=0.015[/tex]. So

[tex]\mathbb P(X\ge6)=1-\mathbb P(X<6)=1-\displaystyle\sum_{x=0}^5\binom{100}x0.015^x(1-0.015)^{100-x}\approx0.0041[/tex]

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