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GGR270H1 (38)
Lecture 5

# Lecture 5 - October 10

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School
University of Toronto St. George
Department
Geography
Course
GGR270H1
Professor
Damian Dupuy
Semester
Fall

Description
Lecture 5 – October 10 Probability II *** – Understanding of the chances of something happening – Probability focuses on the occurence of an event or not happening – Where one of several possible outcomes could result – Outcome are (and must be) mutually exclusive – either happens or it doesnt – CANNOT have 3 or 2 possibilities – Can be thought of as frequency of an event occuring relative to all other outcomes P(A)= F(A)/ F(E) where.... – P(A) = Probability of outcomeAoccuring – F(A) =Abosoute frequency ofA – F(E) = Frequency of all outcomes Probability – Example 1 – Die has 6 faces numbered 1-6 – What is the likelihood of rolling a 6 in one throw? – P(6) = 1/6 or 1 in 6 or 0.167 (if you multiply 0.167 by 100 = 16.7 % chance) – Same probability exists for each of the other outcomes too. Probability – Example 2 – Examine the record of wet and dry days over a 100 day period – 62 days recorded dry – 38 days recorded as wet – What is the Probability of a wet day occuring/ – P(wet) = # of wet days/ total # of days = 38/100 = .38 – Can also say 38% chance a wet day will occur. – Alternatively, Probability of a Dry day occuring is... – P(dry) = 62/100 = .62 – Can also say 62% chance to get dry days Probability 3 – RULES – Maximum probability of an outcome is 1.0 – all Probabilities msut add up to 1 or ... – 0.0 < P(A) < 1.0 First rule – Addition Rule – Used when finding probability of a single independent events – P (Aor B) = P(A) + P (B) – anytime you have ' or' you dealing with addition rule Probability – Addition Rule (when you see (the word – Or) know its addition rule) (PUT ON EXAM) – P(a or b) = P (a) + P (b) – What is the probability of rolling a 6 or a 5 in a single throw? P (6) = .167 P (5) = .167 – Therefore Probability of a 5 OR a 6 = P (6) + P (5) or 0.167 + 0.167 = 0.334 or a 33.4 % chance of throwing a 6 or a 5 in a single throw – Probability of throwing a 5 or 6 or 4 = .167 + .167 +.167 = .501 Probability 4 - Rules continued – Multiplication Rule WHEN YOU SEE AND IS MULTIPLICATION (PUT ON EXAM) – Used when finding probability of multiple independent events P (Aand B) = P(A) x P(B) – example what is the probability of throwing a die and getting two 6s or one 5 and one 6 Probability – Multiplication Rule – P(a and b) = P (a) x P (b) – What is the probability of rolling two sixes in subsequent throws? P(6) = .167 P(6) = .167 – Therefore, the probability of a 6 and a 6 = P(6) x P (6) or .167 x .167 = .02778 Or a 2.8% chance of throwing a 6 or a 5 in a single throw – Probability of throwing 3 sixes in a row = .167 x .167 x .167 = .00463 or approx 1/2 of 1% chance Why you need to know everything mentioned above? Probability and Probability Distributions Probability Distributions – Often see consistent or typical patterns of probabilities in certain situations – These are called Probability Distributions – Similar to frequency distributions – (DIFFERE
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