Probability Theory

Question 1

∈?

Answer 1

Included in the set

Question 2

a c b?

Answer 2

-a is a subset of b

Question 3

A n (B u C)?

Answer 3

(A n B) u (A n C)

Question 4

A u (B n C)?

Answer 4

(A u B) n (A u C)

Question 5

(AnB)^c ?

Answer 5

A^c u B^c

Question 6

(AuB)^c?

Answer 6

A^c n B^c

Question 7

Equation for mutual exclusive?

Answer 7

A∩B =∅

Question 8

AnB meaning?

Answer 8

-both a and b happen

Question 9

A u B meaning?

Answer 9

-either A or B happens

Question 10

If a and b are pairwise disjoint (cannot both happen) what is probability of their union?

Answer 10

-sum of each probability

Question 11

Axioms of probability?

Answer 11

Axiom 1: P(A) ≥ 0 for all events A.

Axiom 2: P(S) = 1.

Axiom 3: pairwise disjoint union rule

Question 12

P(AuB)?

Answer 12

P(A) + P(B) - P(AnB)

Question 13

Ordered with replacement?

Answer 13

n^k

Question 14

Ordered without replacement?

Answer 14

n! / (n-k)!

Question 15

Unordered with replacement?

Answer 15

(n+k-1)
( k )

Question 16

Unordered without replacement?

Answer 16

(n) = n! / k! (n-k)!
(k)

Question 17

Independent when?

Answer 17

P(AnB) = P(A)P(B)

Question 18

Mutually exclusive?

Answer 18

-A ∩ B = ∅,
- P(A∩B) =0

Question 19

P(AlB)?

Answer 19

P(AnB) / P(B)

Question 20

Chain rule?

Answer 20

P(A1 n A2 n A3 …)

= P(A1) P(A2 l A1) P(A3 l A1 A2)

Question 21

Total probability?

Answer 21

-use chain rule

-sum all paths to A

Question 22

Bayes theorem intuition?

Answer 22

-working probability of one of multiple pathways to a probability

Question 23

Bayes theorem equation if two pathways to A?

Answer 23

P(BlA) = P(AnB) / P(A)

= (AlB)P(B) / P(AlB)P(B) + P(AlB^c)P(B^C)