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Lecture 5

# Lecture 5 - October 10

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University of Toronto St. George

Geography

GGR270H1

Damian Dupuy

Fall

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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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