Pieces of aluminium are classified according to the finishing of the surface and

Question

Pieces of aluminium are classified according to the finishing of the surface and according to the
finishing of edge. The results from 85 samples are summarized as follows:

Pieces of aluminium are classified g to the finishing of the surface and according to the finishing of edge. The results from 85 samples are summarized as follows: Edge Surface excellentgood 60 16 good Let A denote the event that a selected piece has "excellent surface, and let B denote the event that a selected piece has "excellent" edge. If samples are selected randomly, determine the following probabilities: (a) P(A) (d) PAnB (g) If the selected piece has excellent edge finishing, what is the probability that it has excellent surface (c) P(A) () P(A UB) (b) P(B) PAUB (h) (i) finishing? If the selected piece has good surface finishing, what is the probability that it has excellent edge finishing? Are A and B independent?

Explanation / Answer

a)

P(A) = (60+5)/85 = 0.764705882 [answer]

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b)

P(B) = (60 + 16)/85 = 0.894117647 [answer]

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c)

P(Ac) = 1 - P(A) = 0.235294118 [answer]

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d)

P(A n B) = 60/85 = 0.705882353 [answer]

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e)

P(A U B) = (60 + 16 + 5) / 85 = 0.952941176 [answer]

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