BUSS1020 Chapter Notes - Chapter 4: Collectively Exhaustive Events, Mutual Exclusivity, Empirical Probability
28 May 2018
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CHAPTER 4: BASIC PROBABILITY
BASIC PROBABILITY CONCEPTS:
• Probability: the chance, likelihood or possibility that an uncertain event will occur (0-1)
o Impossible event P = 0 o Certain event P = 1
• Fundamental Theorem of Probability:
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• Assessing Probability:
o A priori: based on prior knowledge of process à e.g. if all outcomes are equally likely
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o Empirical probability: estimated from observed data
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o Subjective probability: based on an individual’s past experience, personal opinion and/or analysis of a
particular situation
• Events: each possible outcome of a variable
o Simple event: described by a single characteristic
o Joint event: an event described by 2+ characteristics
o Complement of an event: all events not in A =
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• Sample space: collection of all possible events
• Marginal/Simple probability: probability of a simple event occurring à
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• Joint probability: probability of a joint event occurring à
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• Mutually Exclusive: events that cannot occur simultaneously à e.g. H and T
• Collectively Exhaustive: set of events covers the entire sample space
• General Addition Rule:
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o Mutually exclusive events:
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CONDITIONAL PROBABILITY:
• The probability of one event, given another event has occurred
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• Independence: when the outcome of one event DOES NOT affect the
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o Two events, A and B, are independent ONLY IF:
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• Marginal Probability:
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o Where B1, B2 …. Bk are k mutually exclusive and collectively exhaustive events
BAYES’ THEOREM:
• Used to revise existing probabilities based on new information à extension of conditional probability
o Allows us to reverse the conditioning b/w 2 events
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COUNTING RULES:
• RULE 1: if any one of k events can occur on each of n trials,
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o If you roll a dice 3 times, then there are 63 = 216 possible outcomes
• RULE 2: 1st trial has k1 events, 2nd has k2 events…nth trial has kn events, then number of possible outcomes is:
o 8cQ:8cS:+d+8cU:
o How many possibilities are there when a number plate has 3 letters followed by 3 numbers (0 to 9)
§ (26)(26)(26)(10)(10)(10) = 17 576 000 possibilities
• RULE 3: number of ways n items can be arranged in unique order
o Ue+"+8U:8U+f+Q:+d+8Q: 0! = 1
P(A|B) = conditional probability of
A given B
B = event of interest
A = new event which might impact P(B)
