STAT 251 Lecture Notes - Lecture 4: Fair Coin, Posterior Probability, Sample Space
Chapter 3 contd...
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Approaches to Assigning ProbabilitiesâŚ
Classical approach: Assigning probabilities based on the
assumption of equally likely outcomes
Relative frequency: Assigning probabilities based on
experimentation or historical data.
Subjective approach: Assigning probabilities based on the
assignorâs judgment.
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Example: If 85% of Canadian like either baseball or hokey,
65% like baseball and 45% like hokey, what is the
probability that a randomly chosen Canadian likes
baseball and Hokey?
Let A: likes baseball,
B: likes hockey
P(A) = 0.65, P(B) = 0.45, P(A ⪠B ) = 0.85
Need to find P(AâŠB) = ?
Use addition Rule:
P(A ⪠B) = P(A) + P(B) - P(A ⊠B)
0.85 = 0.65 + 0.45 - P(A ⊠B)
P(A ⊠B) = 0.25 2
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Conditional Probability
ďConditional probability is used to determine how two events are
related; that is, we can determine the probability of one event
given the occurrence of another related event.
ďFor any two events, A and B with P(B) > 0, the conditional
probability of A given that B has occurred written as P(A | B)
and read as âthe probability of A given Bâ and is calculated by
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Document Summary
Classical approach: assigning probabilities based on the assumption of equally likely outcomes. Relative frequency: assigning probabilities based on experimentation or historical data. Subjective approach: assigning probabilities based on the assignor"s judgment. Example: if 85% of canadian like either baseball or hokey, P(a) = 0. 65, p(b) = 0. 45, p(a b ) = 0. 85. P(a b) = p(a) + p(b) - p(a b) 0. 85 = 0. 65 + 0. 45 - p(a b) Conditional probability is used to determine how two events are related; that is, we can determine the probability of one event given the occurrence of another related event. Notice that if we rearrange the equation above we get the. Two events, a and b are independent if knowing that one occurs does not change the probability that the other occurs. The probability of a is the same when we are given that b has occurred. Two events a and b are independent if and only if.
