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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