What a Concept
Bayes' Theorem describes the probability that...
The cause is true given an outcome (reverses conditional probability)
What is the Equation for Bayes' Theorem?
P(B|A) = P(A|B)P(B)/P(A)
What is Bayes' Theorem's primary use in civil engineering?
Updating old probabilities based on new data
The probability that a certain building is finished on time is 0.7. The company doing the construction is in the process of hiring a several new workers. The probability that these workers are hired before the construction deadline is 0.6, and the probability the building is finished in this case jumps to 0.9. What is the probability that the new workers are hired if the building is completed on time?
0.77
How are the two conditional probabilities used in Bayes' theorem related
They are inverses (P(A|B) vs P(B|A))
What is the numerator of Bayes' Theorem equal to (Given 2 events A and B)?
P(AnB) (probability of A and B)
Which Bayes' Theorem scenarios are most related to civil engineering (select all that apply)?
A. Screening for a disease and determining the probability a person is sick given a positive test
B. Determining which of three steel foundries a batch of steel came from given it is defective
C. determining the intensity of a storm given that a building survives
B and C
The probability that a train departs New Brunswick, NJ on time is 0.9. There is a 0.87 probability that the train will then arrive at New York Penn Station on time. The probability that the train departed on time given it arrives on time is 0.7. what is the probability the train doesn't arrive on time given it departs on time?
0.32
What theorem is used to find the denominator of the Bayes Theorem equation?
Total Probability Theorem
Given P(A|B), P(A), P(B), How would you find P(BC|A)?
1-P(A|B)P(B)/P(A)
Which subdiscipline of civil engineering would not use Bayes' Theorem?
None of them
The probabilities of a storm being weak, medium, or severe are 0.75, 0.22, and 0.03. The probabilities of a given building being destroyed are 0.02 if the storm is weak, 0.23 if the storm is medium, and 0.75 if the storm is severe. If the building is destroyed, what is the probability that the storm was severe?
0.26
When using a Total Probability Theorem to find the denominator of Bayes' Theorem, what must be true of each event?
They must be mutually exclusive
Given P(A), P(B), and P(A|BC), what additional information would need to be provided for you to find P(AC|B)?
None
If an engineer is attempting to figure out the probability that a structure that failed during an earthquake is made of wood, what is one piece of additional information that he needs?
probability of failure of structures of different materials during an earthquake, probability that a structure is made of different materials.
Out of a set of tributaries to a large river, the probabilities that a given stream has been designated not contaminated, somewhat contaminated, or heavily contaminated are 0.15, 0.45, and 0.40 respectively. The probabilities that a stream supports aquatic life given its condition are 0.99, 0.64, and 0.11 respectively. What is the probability that a stream is not comtaminated given it doesn't support life?
0.0029
Do you need Bayes' Theorem if A and B are independent?
No
What do the expressions P(A|B)P(B) and P(B|A)P(A) have in common?
Both equal P(AnB)
Which civil engineering subdiscipline is most likely to use Bayes' Theorem?
Structural engineering (according to Google)
Three different train lines, Northeast Corridor (NEC), Montclair-Boonton (MB), and Pascack Valley (PV), all meet up at Newark Penn Station. The probabilities that a given train from each line arrives on time are 0.84, 0.80, and 0.78 respectively. The probability that the NEC and MB trains arrive on time given the PV train is late is 0.624. What is the probability that the NB train is late given the other two arrive on time?
0.16 (Trick Question, all three events are independent so the answer is 1-P(N))