Question

In: Statistics and Probability

A system consists of three components, namely Component A, Component B and Component C, placed in...

A system consists of three components, namely Component A, Component B and Component C, placed in series. A study revealed the following information:

(i) The probability that Component A fails in a week is 0.023;

(ii) The probability that Component B fails in a week is 3 times the probability that both Component B and Component C fail in a week;

(iii) the probability that Component C fails in a week is 9 times the probability that Component A and Component B but not Component C fails in a week;

(iv) The probability that Component A and Component B fail in a week is 0.005;

(v) The probability that Component A and Component C fail in a week is 4 times the probability that all three components fail in a week;

(vi) The probability that Component B or Component C but not both fail in a week is 0.033;

(vii) The probability that all three components fail in a week is 0.002.

(a) Construct a Venn diagram for the above situation with clear definition of events and probabilities shown.

(b) Calculate the probability that no component fails in a week.

(c) If there is exactly one component failed in a week, what the probability that the failed component is Component A?

Expert Solution

orchestra answered 2 years ago

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