Question

Suppose that the probability that a fluorescent light will have a useful life of at least 500 hours is 0.85. Suppose you have 10 of these fluorescent lights in your workshop. Find the following probabilities:

a. The probability that 8 of these will have a useful life of at least 500 hours.

b. The probability that at most 2 of them will not have a useful life of 500 hours.

Answer 1

Sample size , n =    10
Probability of an event of interest, p =   0.85

Binomial probability is given by

P(X=x) = C(n,x)*px*(1-p)(n-x)

P ( X =    8   ) = C(10,8) * 0.85^8 * (1-0.85)^2 =            0.2759

.............

b)

Sample size , n =    10
Probability of an event of interest, p =   0.15

	X	P(X)
P ( X = 0) = C (10,0) * 0.15^0 * ( 1 - 0.15)^10=	0	0.1969
P ( X = 1) = C (10,1) * 0.15^1 * ( 1 - 0.15)^9=	1	0.3474
P ( X = 2) = C (10,2) * 0.15^2 * ( 1 - 0.15)^8=	2	0.2759

p(x<=2) = 0.1969 + 0.3474 + 0.2759  

= 0.8202

..................

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