MATH 140 Lecture Notes - Lecture 8: 5,6,7,8, Empty Set
Yellow = Formulas; Turquoise = Definitions
February 23rd Notes
Chapter 5 Probability
- Probability Examples
o Probability of Flipping Heads = 1/2
o Probability of Rolling a 6 = 1/6
o Probability of Picking a King = 4/52
o Probability of Picking a Diamond = 13/52
- P(A) = m/n
o A = outcome or event
o m = number that favors A
o n = total number
- Definitions
o Experiment: the outcome
o Trials (n): how many times you do something
o Equally Likely: all outcomes have the same probability
o Mutually Exclusive: if one thing happens, it can happen again, but not at the same
time
o Independent: nothing in common
o Dependent: something in common
o Exhaustive: all possible cases
- Variables
o U = union
o Π = intersection
o C = subset
o C = equal set
Conditional Probability Example #1
4 Red
P(R) = 4/10
6 Green
P(R|R) = 3/9
P(R|G) = 4/9
- Simple Event: 1 outcome
o Example: flipping for heads or tails
- Compound Event: more than 1 outcome
o Example: rolling a dice to find probability of odds or evens
- Additive Law: either this or that probability
o P(AUB) = P(A) + P(B)
o A and B are mutually exclusive
§ P(K) = 4/52
§ P(Q) = 4/52
• Either King or Queen (mutually exclusive)
o P(KUQ) = P(K) + P(Q)
o P(KUQ) = 4/52 + 4/52
o P(KUQ) = 8/52
Document Summary
Probability examples: probability of flipping heads = 1/2, probability of rolling a 6 = 1/6, probability of picking a king = 4/52, probability of picking a diamond = 13/52. P(a) = m/n: a = outcome or event, m = number that favors a, n = total number. Variables: u = union, = intersection, c = subset, c = equal set. Simple event: 1 outcome: example: flipping for heads or tails. Compound event: more than 1 outcome: example: rolling a dice to find probability of odds or evens. Additive law: either this or that probability: p(aub) = p(a) + p(b, a and b are mutually exclusive. P(q) = 4/52: either king or queen (mutually exclusive, p(kuq) = p(k) + p(q, p(kuq) = 4/52 + 4/52, p(kuq) = 8/52. Yellow = formulas; turquoise = definitions: either king or diamond (not mutually exclusive, p(a) + p(b) = p(a b, p(kud) = p(k) + p(d, p(kud) = 4/52 + 13/52 1/52, p(kud) = 16/52.
