ESBE4eAISEsm04 - Chapter 4 Introduction to Probability...

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Unformatted text preview: 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 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. Chapter 4 Solutions: 1. Number of experimental Outcomes = (3) (2) (4) = 24 2. 6 3 6! 3 3 6 5 4 3 2 1 3 2 1 3 2 1 20 F H G I K J = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ! ! ( )( ) ABC ACE BCD BEF ABD ACF BCE CDE ABE ADE BCF CDF ABF ADF BDE CEF ACD AEF BDF DEF 3. 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 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 3 6 6! 6 3 6 5 4 120 = − = = ( )! ( )( )( ) BDF BFD DBF DFB FBD FDB 6. P (E 1 ) = .40, P(E 2 ) = .26, P(E 3 ) = .34 The relative frequency method was used. 4 - 2 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. Introduction to Probability 7. 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 The classical method was used. 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 4 50! 4 46! 50 49 48 47 4 3 2 1 230 300 F H G I K J = = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ = ! , 10. a. Use the relative frequency approach: P(California) = 1,434/2,374 = .60 b. Number not from 4 states = 2,374 - 1,434 - 390 - 217 - 112 = 221 P(Not from 4 States) = 221/2,374 = .09 c. P(Not in Early Stages) = 1 - .22 = .78 d. Estimate of number of Massachusetts companies in early stage of development = (.22)390 ≈ 86 4 - 3 This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not This edition is intended for use outside of the U....
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This note was uploaded on 05/26/2010 for the course ACC 251 taught by Professor Carl during the Winter '09 term at University of Central Arkansas.

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ESBE4eAISEsm04 - Chapter 4 Introduction to Probability...

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