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p chapter 3 solutions 3rd ed fall 2007

# p chapter 3 solutions 3rd ed fall 2007 - Probability Third...

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Sheet1 Page 1 Probability, Third Edition By David J Carr & Michael A Gauger Published by BPP Professional Education Solution 3.1 We require Pr ()Band Pr (AnB). We have: ( ) () () (n) () (AB)Pr (n) Pr A.B Err:509 AB Err:509 AB ) 0.75 =0.39 +3Pr (AB) . n Pr (AB)=0.12 B=0.48 . n ,Pr () From the definition of conditional probability: (n) 0.12 Pr AB Pr (AB)= 0.25 Pr ()B 0.48 Solution 3.2 We have: Pr (AB ) Pr APr B Solutions to practice questions h Chapter 3

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Sheet1 Page 2 n (') () Pr (BA')== Err:509 Pr A' Intuitively, since Aand B are independent, Pr (BA')=Pr (B). ()A' Pr () Solution 3.3 Let A be the event that the first student selected is a man, and let B be the event that the second student selected is a man. Then: Pr (n) Pr() B AB APr( A) Pr (AB)= Err:520 (6/10 )(5/9 ) 5 Pr()B Pr ()APr (BA)+Pr ()'Pr ( AB A) Err:520 Err:520 6/10 5/9 +4/10 6/9 9 Note: Intuitively, if we know that the second student selected is a man, the probability that the first student selected is a man is 5 (the number of men remaining) divided by 9 (the number of students remaining).
Sheet1 Page 3 ( )()( )() ) Solution 3.4 Let N represent nausea and let V represent impaired vision. Then we have: Pr (n ) Pr ()V -Pr (VN ) Pr (VN')= VN = n Pr N' () N' Pr () 0.63 -0.32 0.76 10.59 - Solution 3.5 The probabilities are shown in the following Venn diagram: C I 0.06 S T 0.23 0.08 0.04 0.11 0.1 0.22 0.16 Hence we have: Probability Solutions to practice questions h Chapter 3

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Sheet1 Page 4 Pr (C (I'T )) 0.22 n n Pr ( (I'nT') C )= 0.34 Pr ()C 0.64 Solution 3.6 If 60% of the policies are for male lives, then 40% are for female lives. Of the policies for male lives, 15% have sums assured in excess of \$500,000. Hence in absolute terms, 60% 15% =9% of all policies are for male lives and with sums assured in excess of \$500,000, and 60% -9% =51% are for male lives and with sums assured below \$500,000. Using a similar method, the full breakdown of the policies is as follows:
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