Math Assignment #2
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 (
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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)
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The probability that an HRO does not have employee absenteeism nor employee turnover is 0.26. 3.84
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The probability that the current sleep stage is REM given that the previous sleep stage was Wake is 0.022. (b)
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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): ( (
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(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(I) = 0.01 P(IC) = 0.99 P(D|IC) = 0.01 P(DC|IC) = 0.99 )( ) ( | ) ( ) ( ( ) ( ) The probability that either a jet fire or a flash fire will occur is 0.02. 3.132 (a) ( )( )( )( )( )( ) This system allowed 17,576,000 license plates. (b) ( )( )( )( )( )( )
This new system provided 17,576,000 new license plates (c) The total number of licenses available for registration in Florida is 35,152,000 license plates. 3.148 (a) Let H = the event that a person has HIV in North America Let pos = the event that the HIV test yields positive ( | ) ( ) ( | ) ( | ) ( ) ( | ) ( ) ( )( ) ( )( ) ( )( ) (b)Let HA = the event that a person has HIV in Asia ( | ) ( ) ( | ) ( | ) ( ) ( | ) ( ( )( ) ( )( ) ( )( )
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(c)Let H = the event that a person has HIV in North America Let P1 = the event that the first HIV test is positive Let P2 = the event that the second HIV test is positive ( | ) ( ) ( | ) | ) ( ) ( | ) ( ), ( , ( | ) ( | )- ( ) *, ( | ) ( | )- ( ) , ( | ) ( | ,( )( )-( ) ,( )( )-( ) ,( )( )-(
(d)Let H = the event that a person has HIV in Asia Let P1 = the event that the first HIV test is positive Let P2 = the event that the second HIV test is positive ( | ) ( ) ( | ) | ) ( ) ( | ) ( , (
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3.178 (a) Let F = the event that the wheelchair user had an injurious fall ( ) (b)Let 5 = the event that the wheelchair user had all five features installed in the home
( ) (c)Let F = the event that the wheelchair user had an injurious fall Let N = the event that the wheelchair user had no features installed in the home (
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The probability that the wheelchair user had no falls and none of the features installed in the home is 0.291. (d)
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Given no features installed in the home, the probability for an injurious fall is 0.183.
3.190 (a) (
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The probability that the dealer will draw a blackjack is 0.036. (b)Let D = the event that the dealer gets blackjack given that the player already has blackjack P(D) ( ) P(DC) ( ) ( ) The probability that the player will win with a blackjack is 0.0352.
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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)
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The probability that an HRO does not have employee absenteeism nor employee turnover is 0.26. 3.84
(a)
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The probability that the current sleep stage is REM given that the previous sleep stage was Wake is 0.022. (b)
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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): ( (
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(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(I) = 0.01 P(IC) = 0.99 P(D|IC) = 0.01 P(DC|IC) = 0.99 )( ) ( | ) ( ) ( ( ) ( ) The probability that either a jet fire or a flash fire will occur is 0.02. 3.132 (a) ( )( )( )( )( )( ) This system allowed 17,576,000 license plates. (b) ( )( )( )( )( )( )
This new system provided 17,576,000 new license plates (c) The total number of licenses available for registration in Florida is 35,152,000 license plates. 3.148 (a) Let H = the event that a person has HIV in North America Let pos = the event that the HIV test yields positive ( | ) ( ) ( | ) ( | ) ( ) ( | ) ( ) ( )( ) ( )( ) ( )( ) (b)Let HA = the event that a person has HIV in Asia ( | ) ( ) ( | ) ( | ) ( ) ( | ) ( ( )( ) ( )( ) ( )( )
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(c)Let H = the event that a person has HIV in North America Let P1 = the event that the first HIV test is positive Let P2 = the event that the second HIV test is positive ( | ) ( ) ( | ) | ) ( ) ( | ) ( ), ( , ( | ) ( | )- ( ) *, ( | ) ( | )- ( ) , ( | ) ( | ,( )( )-( ) ,( )( )-( ) ,( )( )-(
(d)Let H = the event that a person has HIV in Asia Let P1 = the event that the first HIV test is positive Let P2 = the event that the second HIV test is positive ( | ) ( ) ( | ) | ) ( ) ( | ) ( , (
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3.178 (a) Let F = the event that the wheelchair user had an injurious fall ( ) (b)Let 5 = the event that the wheelchair user had all five features installed in the home
( ) (c)Let F = the event that the wheelchair user had an injurious fall Let N = the event that the wheelchair user had no features installed in the home (
)
The probability that the wheelchair user had no falls and none of the features installed in the home is 0.291. (d)
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Given no features installed in the home, the probability for an injurious fall is 0.183.
3.190 (a) (
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The probability that the dealer will draw a blackjack is 0.036. (b)Let D = the event that the dealer gets blackjack given that the player already has blackjack P(D) ( ) P(DC) ( ) ( ) The probability that the player will win with a blackjack is 0.0352.
