1) A serial system is comprised of 5 components connected in series. In order fo

Question

1) A serial system is comprised of 5 components connected in series. In order for the serial system to work, all five components must function correctly. Assume that each component fails to nts. The probability with which each component fails is 0.01 (a) What is the probability that the whole system functions correctly? (b) What is the probability that at most 3 of the 5 components fail? (c) Let X denote the number of components that fail to function. Find the probability mass function of X. (d) Let Y be a Bernoulli random variable that is equal to 1 if at least 4 components function correctly. Find the probability mass function of Y

Explanation / Answer

(a) Probability that a component works = 1 - 0.01 = 0.99

Probability that the whole system works = 0.995 = 0.9510.

(b) Probability that atmost three will fail from binomial table (p = 0.01 n = 5)

P(x <= 3) = 0.99999.....

(c)

(d)

X P(X) 0 0.9510000000 1 0.0480298005 2 0.0009702990 3 0.0000098010 4 0.0000000495 5 0.0000000001

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