Probability 101

Colloquial:
Epistemic or Subjective

Decimal
Expression

Expressed
as a Ratio

Expressed as a
Percentage

Expressed as
Wagering Odds

Colloquial:
Objective or Frequeny

Certainly True

1.0

1

100%

not applicable

Always so, or necessarily

Almost Certainly True

0.9

9/10

90%

1|9

Almost Always

Very Probably True

0.67

2/3

67%

1|2

Very Frequently

Probably True

0.51

51/100

51%

49|51

Usually
"most commonly"

Can't Tell

0.5

1/2

50%

1|1
even odds

Equiprobably
"it's a toss up"

Probably False

0.49

49/100

49%

51|49

Usually not

Very Probably False

0.33

1/3

33%

2|1

Very Seldom

Almost Certainly False

0.1

1/10

10%

9|1

Almost Never

Certainly False

0.0

0

0%

not applicable

Never, or
impossibly

Example: Assuming a Standard Deck of Cards {52 cards in four suits valued A to K}

Basic Theorems

Online Problems

Advanced Problem

Example: Problem 5 of More Probabilitiy Problems: According to the Consumer Reports website, Consumer Union did a nationwide survey of owners of manufactured (mobile) homes. The report determined that 6 out of 10 (or 60%) of the people had major problems with their homes. If 5 manufactured home owners are randomly selected, what is the probability that at least one of them had major problems with their homes?

Solution by Multiplication plus Negation:

  1. p(P|Q|R|S|T) = 1 - p(not-(P|Q|R|S|T)) {negation theorem}
  2. p(not-(P|Q|R|S|T)) = p(not-P & not-Q & not-R & not-S & not-T) {equivalence}
  3. p(not-P & not-Q & not-R & not-S & not-T) = (.4*.4*.4*.4*.4) = .01 {applying the multiplication theorem}
  4. p(P|Q|R|S|T) = .99 {applying the negation theorem}