Chapter 4 terms

Question 1

Conditional probability

Answer 1

Event A occurs given Event B has occurred
“the chance of observing one of the elements in A, from the set of elements in B only”.

P(A|B) = P(AnB)/P(B)
= P((AnB)/sample space)/(P(B)/sample space)

Question 2

Partition theorem take 2

Answer 2

P(A) =E^m_i=1 P(AnB_i) = E^m_i=1 P(A|B_i)P(B_i)

Question 3

probability trees

Answer 3

Useful when events happen in a sequence

Multiple across the branches

Question 4

Eikosogram

Answer 4

A scaled representation of a two-way of counts. Displayed as a square. with side of length one

Question 5

Independence

Answer 5

Knowing that B occurs does not affect the probability of A occurring.

P(A|B) = P(A)
P(B|A) = P(B)
Independent if P(AnB) = P(A) P(B)

if P(B|A) = P(BnA)/P(A) = P(A|B)P(B)/P(A) = P(B)
then
P(AnB) = P(A|B)P(B) = P(A)P(B)

Question 6

Mutually exclusive

Answer 6

AnB = (/), which implies P(AnB) = 0