# Chap 4 - Chapter 4 Introduction to Probability Learning...

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Chapter 4 Introduction to Probability Learning Objectives 1. Obtain an appreciation of the role probability information plays in the decision making process. 2. Understand probability as a numerical measure of the likelihood of occurrence. 3. Know the three methods commonly used for assigning probabilities and understand when they should be used. 4. Know how to use the laws that are available for computing the probabilities of events. 5. Understand how new information can be used to revise initial (prior) probability estimates using Bayes’ theorem. 4 - 1

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Chapter 4 Solutions: 1. Number of experimental Outcomes = (3)(2)(4) = 24 2. 6 6! 6 5 4 3 2 1 20 3 3!3! (3 2 1)(3 2 1)   × × × × × = = =  ÷ × × × ×   ABC ACE BCD BEF ABD ACF BCE CDE ABE ADE BCF CDF ABF ADF BDE CEF ACD AEF BDF DEF 3. P 3 6 6! 6 3 6 5 4 120 = - = = ( )! ( )( )( ) BDF BFD DBF DFB FBD FDB 4. a. H T H T H T H T H T H T H T (H,H,H) (H,H,T) (H,T,H) (H,T,T) (T,H,H) (T,H,T) (T,T,H) (T,T,T) 1st Toss 2nd Toss 3rd Toss b. Let: H be head and T be tail (H,H,H) (T,H,H) (H,H,T) (T,H,T) (H,T,H) (T,T,H) (H,T,T) (T,T,T) c. The outcomes are equally likely, so the probability of each outcomes is 1/8. 5. P (E i ) = 1/5 for i = 1, 2, 3, 4, 5 P (E i ) 0 for i = 1, 2, 3, 4, 5 P (E 1 ) + P (E 2 ) + P (E 3 ) + P (E 4 ) + P (E 5 ) = 1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1 4 - 2
Introduction to Probability The classical method was used. 6. P (E 1 ) = .40, P (E 2 ) = .26, P (E 3 ) = .34 The relative frequency method was used. 7. No. Requirement (4.4) is not satisfied; the probabilities do not sum to 1. P (E 1 ) + P (E 2 ) + P (E 3 ) + P (E 4 ) = .10 + .15 + .40 + .20 = .85 8. a. There are four outcomes possible for this 2-step experiment; planning commission positive - council approves; planning commission positive - council disapproves; planning commission negative - council approves; planning commission negative - council disapproves. b. Let p = positive, n = negative, a = approves, and d = disapproves . Planning Commission Council p n a d a d (p, a) (p, d) (n, a) (n, d) 9. 50 50! 50 49 48 47 230,300 4 4!46! 4 3 2 1 × × × = = = ÷ × × × 10. a. Use the relative frequency approach. The percent tells us that 94 out of 100 Morehouse students graduate with debt. P ( Debt) = .94 b. Use the relative frequency approach. Five of the 8 schools have over 60% of their students graduating with debt. 4 - 3

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Chapter 4 P (School with over 60%) = 5/8 = .625 c. Use relative frequency approach. P (School with average debt > \$30,000) = 2/8 = .25 d. P (No debt) = 1 - .72 = .28 e. This is a weighted average; 72% graduate with an average debt of \$32,980 and 28% graduate with an average debt of \$0. Mean debt per student =
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## This note was uploaded on 11/08/2011 for the course MAT/FIN 272 taught by Professor Burns during the Spring '11 term at Central Connecticut State University.

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Chap 4 - Chapter 4 Introduction to Probability Learning...

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