mont4e_sm_ch02_sec08

mont4e_sm_ch02_sec08 - P( A | B) = 2-121. (0.38)(0.53) P( A...

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Unformatted text preview: P( A | B) = 2-121. (0.38)(0.53) P( A ∩ B) P( A) P( B | A) = = = 39.3821% P( B) P( A) P( B | A) + P ( A' ) P( B | A' ) (0.38)(0.53) + (0.62)(0.5) Let G denote a product that received a good review. Let H, M, and P denote products that were high, moderate, and poor performers, respectively. a) P(G) = P(G H ) P( H) + P(G M) P( M) + P(G P) P( P) = 0. 95( 0. 40) + 0. 60( 0. 35) + 0. 10( 0. 25) = 0. 615 b) Using the result from part a., P ( G H ) P ( H ) 0. 95( 0. 40) P( H G ) = = = 0. 618 P(G) 0. 615 c) P ( H G ' ) = P ( G ' H ) P ( H ) = 0. 05( 0. 40) = 0. 052 P(G ' ) 1 − 0. 615 2-122. a) P(D)=P(D|G)P(G)+P(D|G’)P(G’)=(.005)(.991)+(.99)(.009)=0.013865 b) P(G|D’)=P(G∩D’)/P(D’)=P(D’|G)P(G)/P(D’)=(.995)(.991)/(1-.013865)=0.9999 2-123.a) P(S) = 0.997(0.60) + 0.9995(0.27) + 0.897(0.13) = 0.9847 b) P(Ch|S) =(0.13)( 0.897)/0.9847 = 0.1184 Section 2-8 2-124. Continuous: a, c, d, f, h, i; Discrete: b, e, and g Supplemental Exercises 2-125. Let B denote the event that a glass breaks. Let L denote the event that large packaging is used. P(B)= P(B|L)P(L) + P(B|L')P(L') = 0.01(0.60) + 0.02(0.40) = 0.014 2-126. Let "d" denote a defective calculator and let "a" denote an acceptable calculator a a) S = {ddd , add , dda, ada, dad , aad , daa, aaa} b) A = {ddd , dda, dad , daa} c) B = {ddd , dda, add , ada} d) A ∩ B = {ddd , dda} e) B ∪ C = {ddd , dda , add , ada, dad , aad } 2-21 ...
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