STAB22 - Highly detailed Chapter 15 Notes, Summer 2012, Ken Butler

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STAB22 - CHAPTER15 - PROBABILITY RULES!
p395
WHERE ARE WE GOING?
CONDITIONAL PROBABILITY
- ex. probability of car accident happening given the person is
- a senior
- a teenager
- young adult
- probability of an event can change when more is learned about relevant situation
PROBABILITY ON CONDITION
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[1]
(ex) What is the name of the home province of a travelling Canadian to Stonehenge,
England?
S = {Alberta, BC, Manitoba, NFL and Labrador, NWT, Nova Scotia, Nunavut, Ontario,
PEI, Quebec, Saskatchewan, Yukon}
- probability of meeting some1 from Ontario is not the same as probability of meeting
some1 from Nunavut
=> diff. outcomes listed in sample space are NOT equally likely
[2]
- how can these outcomes be combined in diff ways to make diff. events?
(ex)
A = {New Brunswich, NFL & Labrador, Nova Scotia, PEI} => event that person's home
province is one of the Atlantic provinces
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B = {New Brunchswick, NWT, Nunavut, Quebec, Yukon} => event that person's home
province has official lang. being French
[3]
- probabilities of events A and B?
- outcomes in sample space in this situation are not equally likely
=> despite event A having 4 outcomes, each one will not have probability 1/13
to yield 4/13 in total for event.
=> same situation goes for B: does not total to 5/13
CONDITIONAL PROBABILITY - It Depends..
[1]
(ex) contingency table showing distrubution of official language by region
- gives counts of visitors by:
- cvar1: official lang &
- cvar2: region of residence
P(French) = 69/248 = 0.2782
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=> probability that we select French speaker from entire group of visitors = its
corresponding relative freq.
- b/c it is equally likely to select any of 248 ppl at random
P(French and Atlantic) = 0.0362
P(Quebecer) = 0.221774193
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Document Summary

Ex. probability of car accident happening given the person is. Probability of an event can change when more is learned about relevant situation. [1] (ex) what is the name of the home province of a travelling canadian to stonehenge, S = {alberta, bc, manitoba, nfl and labrador, nwt, nova scotia, nunavut, ontario, Probability of meeting some1 from ontario is not the same as probability of meeting some1 from nunavut. => diff. outcomes listed in sample space are not equally likely. How can these outcomes be combined in diff ways to make diff. events? (ex) A = {new brunswich, nfl & labrador, nova scotia, pei} => event that person"s home province is one of the atlantic provinces. B = {new brunchswick, nwt, nunavut, quebec, yukon} => event that person"s home province has official lang. being french. Outcomes in sample space in this situation are not equally likely.

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