Homework#3_Solutions

Homework#3_Solutions - Homework #3 Solutions Topic...

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Unformatted text preview: Homework #3 Solutions Topic Conditional probability and Multiplication rule 287. a) P(A) = 86/100 c) P( A B ) = b) P(B) = 79/100 Assignment 2-87, 89, 90,93, 95, 97, 104, 105, 106 P( A B ) 70 / 100 70 P( B) 79 / 100 79 P( A B) 70 / 100 70 P( A) 86 / 100 86 d) P( B A ) = 289. Let A denote the event that a leaf completes the color transformation and let B denote the event that a leaf completes the textural transformation. The total number of experiments is 300. (a) P ( B | A) B' ) 243 / 300 P( A B) 0.903 P( A) (243 26) / 300 26 / 300 P( A B' ) 0.591 P( B' ) (18 26) / 300 (b) P( A | 290. a) 0.82 b) 0.90 c) 8/9 = 0.889 d) 80/82 = 0.9756 e) 80/82 = 0.9756 f) 2/10 = 0.20 293. Let A denote the event that autolysis is high and let B denote the event that putrefaction is high. The total number of experiments is 100. (a) P ( B' | A) P( A B' ) 18 / 100 0.5625 P( A) (14 18) / 100 1 (b) P ( A | B) P( A B) 14 / 100 0.1918 P( B) (14 59) / 100 (c) P ( A' | B' ) P ( A' B' ) 9 / 100 0.333 P( B' ) (18 9) / 100 295. 297. a)P=(81)/(3501)=0.020 b)P=(8/350) [(81)/(3501)]=0.000458 c)P=(342/350) [(3421)/(3501)]=0.9547 a) 20/100 b) 19/99 c) (20/100)(19/99) = 0.038 d) If the chips were replaced, the probability would be (20/100) = 0.2 2104. Let A denote the event that an egg survives to an adult Let EL denote the event that an egg survives at early larvae stage Let LL denote the event that an egg survives at late larvae stage Let PP denote the event that an egg survives at prepupae larvae stage Let LP denote the event that an egg survives at late pupae stage a) P ( A) 31 / 421 0.0736 b) P ( A | LL ) P ( A LL ) 31 / 421 0.1013 P ( LL ) 306 / 421 c) P ( EL ) 412 / 421 0.9786 P ( LL EL ) 306 / 421 0.7427 P ( EL ) 412 / 421 P ( LL | EL ) 2 P ( PP | LL ) P ( PP LL ) 45 / 421 0.1471 P ( LL ) 306 / 421 P ( LP PP ) 35 / 421 0.7778 P ( PP ) 45 / 421 P ( LP | PP ) P ( A | LP ) P ( A LP ) 31 / 421 0.8857 P ( LP ) 35 / 421 2105. 2106. The late larvae stage has the lowest probability of survival to the prepupae stage. a) P( A B) P( AB)P(B) (0.4)(0.5) 0.20 b) P( A B) P( A B)P(B) (0.6)(0.5) 0.30 P( A ) P( A B) P( A B ) P( A B)P(B) P( A B )P(B ) ( 0.2)( 0.8) ( 0.3 )( 0.2) 0.16 0.06 0.22 3 ...
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This note was uploaded on 02/27/2012 for the course ISE 540:210 taught by Professor Susanalbin during the Spring '12 term at Rutgers.

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