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# math assignment 2.docx

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School
Department
Mathematics & Statistics (Sci)
Course
MATH 203
Professor
Patrick Reynolds
Semester
Fall

Description
Math Assignment #2 3.30 (a) There are 8 sample points: (Public, Bedrock, Below Limit) (Public, Bedrock, Detectable) (Public, Unconsolidated, Below Limit) (Public, Unconsolidated, Detectable) (Private, Bedrock, Below Limit) (Private, Bedrock, Detectable) (Private, Unconsolidated, Below Limit) (Private, Unconsolidated, Detectable) (b) Using R, the probabilities of the sample points are as follows: P(Public, Bedrock, Below Limit) = 0.256 P(Public, Bedrock, Detectable) = 0.184 P(Public, Unconsolidated, Below Limit) = 0.067 P(Public, Unconsolidated, Detectable) = 0.031 P(Private, Bedrock, Below Limit) = 0.363 P(Private, Bedrock, Detectable) = 0.099 P(Private, Unconsolidated, Below Limit) = 0 P(Private, Unconsolidated, Detectable) = 0 (c) Using R, the probability that has a detectable level of MTBE is 0.314. This means that 31.4% of public and private wells have a detectable level of MTBE. 3.60 (a) Let A = the event that an HRO has absenteeism Let B = the event that an HRO has turnover ( ) ( ) ( ) ( ) The probability that an HRO with employee absenteeism or employee turnover is 0.74. (b) Let A = the event that an HRO has absenteeism. ( ) ( ) The probability that an HRO does not have employee absenteeism is 0.45. (c) ( ) ( ) The probability that an HRO does not have employee absenteeism nor employee turnover is 0.26. 3.84 (a) ( | ) The probability that the current sleep stage is REM given that the previous sleep stage was Wake is 0.022. (b) ( | ) 0.978 The probability that the previous sleep stage is not the Wake state given that the current sleep stage is REM is 0.978. (c) The events {previous stage is REM} and {current stage is REM} are not mutually exclusive because they can happen at the same time. Two events are only mutually exclusive if they cannot occur at the same time. (d)No, the events {previous stage is REM} and {current stage is REM} are not independent. If they were independent, then the probability that the previous stage is REM given that the current stage is REM would equal the probability that the previous stage is REM, however they are not (as shown below): ( | ) ( ) ( ) ( ) ( ) (e) No, the events {previous stage is Wake} and {current stage is Wake} are not independent. This is because the probability that the previous stage is wake given the current stage is wake does not equal to the probability that the current stage is wake. 3.96 Let I = the event that the leak ignites immediately Let D = the event that the leak is delayed Let H = the event that the gas cloud disperses Looking for HC P(IC = 0.01 P(I ) = 0.99 P(D|I ) = 0.01 P(D |I ) = 0.99 ( | ) ( ) ( )( ) ( ) ( ) The probability that either a jet fire or a flash fire will occur is 0.02. 3.132 (a) ( )( )( )( )(
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