Propositions and Events
"Either the dog ran around the house or the water was too hot."
What is AvB?
Pr(AvB), where A is "Bill strikes out," B is "Bill gets a base hit," Pr(A) = 2/9 and Pr(B) = 3/5.
What is 37/45?
This is the definition of conditional probability.
What is if Pr(B) > 0, Pr(A/B) = Pr(A&B)/Pr(B)?
The first node in the tree diagram is this scientific term, and the second node in the tree diagram is this judicial term.
What are hypothesis and evidence?
Decision theory deals with these three things.
What are options, alternatives, and probabilities?
"Either both eating a lemon and eating a pair or both throwing a frisbee and throwing a shotput."
What is (A∩B)∪(C∩D)?
Pr(A/B), where B is "choosing urn B," A is "getting an airhead," and urn B contains 10 airheads, 9 mars bars, 5 paydays, 2 almond joys, and 1 box of nerds.
What is 10/27?
This is the the rule for overlap.
What is Pr(AvB) = Pr(A) + Pr(B) - Pr(A&B)?
This is the first formulation of Bayes' Rule.
What is Pr(H/E) = (Pr(H) * Pr(E/H)/((Pr(H) * Pr(E/H)) + (Pr(~H) * Pr(E/~H)))?
This relation between alternatives is asymmetric.
What is the preference relation?
These are the circumstances under which a disjunction is true.
What is if and only if either disjunct is true?
These are the circumstances under which A and B are mutually exclusive.
What is if and only if A&B must be false?
This is the rule for multiplication.
What is if Pr(B) > 0, Pr(A&B) = Pr(A/B) * Pr(B)?
What is Pr(Hj/E) = (Pr(Hj) * Pr(E/Hj))/Σ(Pr(Hi) * Pr(E/Hi))?
This is the principle of rational choice for choice under certainty
What is choose your most preferred alternative?
"The complement of both spelling "indisputability" correctly and spelling "hypostatization" correctly"
What is (A∩B)'?
Pr(A&B), where A is "getting a 7 on the first dive," B is "getting a 3 on the second dive," Pr(A) = 1/46, and Pr(B) = 1/24.
What is 1/1104?
This is the rule for total probability.
What is if 0 < Pr(B) < 1, then Pr(A) = (Pr(B) * Pr(A/B)) + (Pr(~B) * Pr(A/~B))?
A test that says there are allergens present when there are not, for instance
What is a false positive?
This condition asserts that if aPb and bIc, then aPC.
What is the transitivity condition?
"Either both Tom is not a robin or Tom is not a cardinal and Tom is a robin or Tom is a cardinal or Felix is orange and Felix is not hungry."
((~Av~B)&(AvB))v(C&~D)
Pr(AvB), where A is "it's raining," B is "it's thundering," Pr(A) = 3/7, Pr(B/A) = 5/7, and Pr(B/~A) = 1/7
What is 24/49?
This is the definition of statistical independence.
What is if Pr(A) > 0, Pr(B) > 0, A and B are statistically independent iff Pr(A/B) = Pr(A)?
Pr(H/E), where H is "Denton drinks a soda," E is "Denton hiccups" Pr(H) = 2/7, Pr(E/H) = 8/11, and Pr(E/~H) = 1/11
What is 16/21?
What is the small improvements argument?