3. (10 points) One is interented in the the component faile a particular tes doe

Question

3. (10 points) One is interented in the the component faile a particular tes does not actually fail. Event A occurs 035 hte of nn electone c Les A be the event that the event thatthe component displays strain beat withpobaility 0.25, nd evet B occswith pecbalálity sest and B be (1) (5 pointa) Are A and B mutualy exclunive (diniyane)r Whas iw the probabdlity dhat the component either fails or shows strnin in the t nih (2) (6 pointa) What is the probability that the component works perfectly wll 0 displays strain nor fails the test)7

Explanation / Answer

1) Two events are mutually exclusive when they cannot happen at the same time. A is the event the component fails and B is the event that the component shows strain but doesn't fail. So we can say that the two events do not occur at the same time and so they are mutually exclusive.

Required probability = P(A union B) = P(A) + P(B) = 0.25+0.35= 0.6 (Since P(A intersection B) = 0 for mutually exclusive events).

2) Probability that the component does not fail = P(AunionB)^c where c means complement event = 1-P(AunionB) = 1- 0.6 = 0.4

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