the probable is what usually happens. aristotle chapter 6: probability
TRANSCRIPT
Chance experiment: any activity or
situation in which there is uncertainty
about which outcome will result
Fate laughs at probabilities. Bulwer, Lytton E.G.
Sample Space: collection of all
possible outcomes of a chance experiment
Roll a dieS={1,2,3,4,5,6}
Probability is the very guide of life. Cicero
What is the sample space?
1.) Rolling 1 die
2.) Rolling 2 dice
3.) Rolling 2 dice and counting the number of pips face up
4.) Toss a coin
5.) Toss a coin four times and record the results
6.) Toss a coin four times and record number of heads
7.) Flip a coin and roll a die
An event is any collection of outcomes from the sample space of a chance experiment.
– Rolling a prime # E = {2,3,5}
A simple event is an event consisting of exactly one outcome.
Rolling a 6: E = {6}
The rectangle represents the sample space and shaded area represents the event A.
The shaded area represents the event not A.
Union •the event A or B happening•consists of all outcomes that are in at least one of the two events–Rolling a prime # or even number
E={2,3,4,5,6}
BAE
Intersection •the event A and B happening
•consists of all outcomes that are in both events–Drawing a red card and a “2” – E = {2 hearts, 2 diamonds}
BAE
• Two events that have no common outcomes are said to be disjoint or mutually exclusive.
A and B are disjoint events
Some illustrations
A B
C
A B C
A B
C
A, B & C are Disjoint
A B
C
A B C
A B
C
A B Cc
A ∩ B ∩ C
A υ B υ C A ∩ B ∩ Cc
Country-Western songs emphasize three basic themes: love, prison, and trucks. A survey of the local Country-Western radio station produced the following data: 12 songs about a truck driver who is in love while in prison2 about people in prison who are not in love and do not drive trucks8 about people who are out of prison, are not in love, and do not drive a truck13 about a prisoner in love28 about a person in love18 about a truck driver in love16 about truck drivers who are not in prison3 about a truck driver in prison who is not in love
12 songs about a truck driver who is in love while in prison2 about people in prison who are not in love and do not drive trucks8 about people who are out of prison, are not in love, and do not drive a truck13 about a prisoner in love28 about a person in love18 about a truck driver in love16 about truck drivers who are not in prison3 about a truck driver in prison who is not in love
How many songs were about:a.) truck drivers?
b.) prisoners?
c.) truck drivers in prison?
d.) people not in prison?
e.) people not in love?
f.) How many songs were surveyed?