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An experiment can result in one of five equally likely simple events,  E1, E2,    , E5.  Events A, B, and C are defined as follows. A: E1, E5     P(A)  =  0.4   B: E2, E3, E4, E5     P(B)  =  0.8   C: E1, E2     P(C)  =  0.4 Refer to the following probabilities. P(A ∩ B)  =  0.2 P(A|B)  =  0.25 P(B|A)  =  0.5 P(B ∪ C)  =  1 P(B|C)  =  0.5 P(C|B)  =  0.25

An experiment can result in one of five equally likely simple events,  E1, E2,    , E5.  Events A, B, and C are defined as follows. A: E1, E5     P(A)  =  0.4   B: E2, E3, E4, E5     P(B)  =  0.8   C: E1, E2     P(C)  =  0.4 Refer to the following probabilities. P(A ∩ B)  =  0.2 P(A|B)  =  0.25 P(B|A)  =  0.5 P(B ∪ C)  =  1 P(B|C)  =  0.5 P(C|B)  =  0.25

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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An experiment can result in one of five equally likely simple events, 
E1, E2,    , E5.
 Events A, B, and C are defined as follows.
A: E1, E5     P(A)  =  0.4
 
B: E2, E3, E4, E5     P(B)  =  0.8
 
C: E1, E2     P(C)  =  0.4
Refer to the following probabilities.
P(A ∩ B)  =  0.2
P(A|B)  =  0.25
P(B|A)  =  0.5
P(B ∪ C)  =  1
P(B|C)  =  0.5
P(C|B)  =  0.25
Use the Addition and Multiplication Rules to find the following probabilities.
(a)
P(A ∪ B)
P(A ∪ B)
 =      +      −        = 
(b)
P(A ∩ B)
P(A ∩ B) =       · P(B)
 = 
(c)
P(B ∩ C)
P(B ∩ C) =       · P(C)
 = 
Do the results agree with those obtained by listing the simple events in each?
P(A ∪ B) = P({E1, E2, E3, E4, E5})  =  1
P(A ∩ B) = P({E5})  =  0.2
P(B ∩ C) = P({E2})  =  0.2
YesNo    
An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table to answer this question.
  A AC
B 0.37 0.41
BC 0.15 0.07
Refer to the following probabilities.
P(A)  =  0.52
P(B)  =  0.78
P(A ∩ B)  =  0.37
P(A ∪ B)  =  0.93
P(A|B)  =  0.474
P(B|A)  =  0.712
Are events A and B independent? Explain.
Since             , A and B     independent.
An experiment can result in one of five equally likely simple events, E,1, E2, Es. Events A, B, and C are defined as follows. A: E1, Es P(A) = 0.4 B: E2, E3, E4, E5 P(B) = 0.8 C: E1, E2 P(C) = 0.4 Refer to the following probabilities. P(A N B) = 0.2 P(A|B) = 0.25 P(B|A) = 0.5 P(B U C) = 1 P(B|C) = 0.5 P(C|B) = 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(A U B) P(A U B) = ---Select-- + --Select--- ---Select-- (b) P(A N B) P(A N B) = |---Select--- v P(B) = (c) P(B N C) P(B N C) = -Select--- P(C) = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E1, E2, E3, E4. E5}) = 1 P(A N B) = P({E5}) = 0.2 P(B N C) = P({E,}) : = 0.2 Yes No
Transcribed Image Text:An experiment can result in one of five equally likely simple events, E,1, E2, Es. Events A, B, and C are defined as follows. A: E1, Es P(A) = 0.4 B: E2, E3, E4, E5 P(B) = 0.8 C: E1, E2 P(C) = 0.4 Refer to the following probabilities. P(A N B) = 0.2 P(A|B) = 0.25 P(B|A) = 0.5 P(B U C) = 1 P(B|C) = 0.5 P(C|B) = 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(A U B) P(A U B) = ---Select-- + --Select--- ---Select-- (b) P(A N B) P(A N B) = |---Select--- v P(B) = (c) P(B N C) P(B N C) = -Select--- P(C) = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E1, E2, E3, E4. E5}) = 1 P(A N B) = P({E5}) = 0.2 P(B N C) = P({E,}) : = 0.2 Yes No
An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table to answer this question. A AC В 0.37 0.41 BC 0.15 0.07 Refer to the following probabilities. P(A) P(B) = 0.52 = 0.78 P(A N B) P(A U B) P(A|B) P(B|A) = 0.37 = 0.93 0.474 = 0.712 Are events A and B independent? Explain. Since ---Select- A and B ---Select--- v independent.
Transcribed Image Text:An experiment can result in one or both of the events A and B, with the probabilities shown below. Use the probability table to answer this question. A AC В 0.37 0.41 BC 0.15 0.07 Refer to the following probabilities. P(A) P(B) = 0.52 = 0.78 P(A N B) P(A U B) P(A|B) P(B|A) = 0.37 = 0.93 0.474 = 0.712 Are events A and B independent? Explain. Since ---Select- A and B ---Select--- v independent.
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