A system is composed of three components, each of which randomly works or doesn\

Question

A system is composed of three components, each of which randomly works or doesn't work. The system works if at least one component works. Let A denote the event that the first component works, B the second component works, and C the third component works The first component works one-third of the time. The second component works one tenth of the time, independently of the first component. If both of the first two components work then the third component works one time in ten; otherwise, the third component works one-seventh of the time. [4 marks) a) Write the four given probabilities in the defined notation b) Select true or false for the statement. [1 mark) ii. The event that the system works can be written as (A' n B'nC')' [1 mark] [4 marks] i. The events A and B are mutually exclusive. c) Determine the probability that the system works.

Explanation / Answer

Solution

a) P(A) = 1/3

P(B) = 1/10

P(C given A and B wirks) = 1/10

P(C) = 1/7

(b) (i) True, A and B are mutually exckusive

(ii) False

(c) P(system works) = (1/3)(2/3) + (1/10)(9/10) + (1/7)(6/7) + (1/10)(9/10) = 0.5247

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