Question

If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights 

(i) exactly 10 will have a useful life of at least 600 hours; 

(ii) at least 11 will have a useful life of at least 600 hours; 

(iii) at least 2 will not have a useful life of at least 600 hours.

Answer 1

Given n = 12 

Probability that a fluorescent light has a life of atleast of 600 hours is p = 0.9 

∴ q = 1 – p = 1 – 0.9 = 0.1 

Let ‘X’ be the number of bulbs. 

∴ Probability of ‘x’ successes in ‘n’ trials is

(i) Probability that exactly 10 bulbs will have a useful life of atleast 600 hours

(ii) Probability that atleast 11 will have a useful life of atleast 600 hours is

(iii) Probability that atleast 2 will not have a useful life of 600 hours is