Response of a certain composite material to high levels of stress is analyzed. I

Question

Response of a certain composite material to high levels of stress is analyzed. It is known that two different types of cracks, A and B, can develop in the material. The probability that a crack of type A develops is 0.4, the probability that a crack of type B develops is 0.3, and the probability that cracks of both types develop is 0.1. Using the set-theoretical language, describe each of the following events. Then, compute the probability of the events. You can use either the formulas or a Venn diagram a) a crack develops in the material b) only a crack of type A develops. c) the material stays intact. d) a crack of type B does not develop.

Explanation / Answer

a)a crack develpos in the material is either A or B crack or both

P(A u B) =P(A)+P(B)-P(A n B)=0.4+0.3-0.1 =0.6

b)only crack of type A and not of B type

P(A n B') =P(A)-P(A n B)=0.4-0.1=0.3

c) there is no crack

P(A' n B') =1-P(A U B) =1-0.6 =0.4

d)

no B type crack

P(B') =1-P(B )=1-0.3 =0.7

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