8-1: Sample Spaces, Events and Probability
Objectives:
1. Definition of probability
2. Applications
A sample space is the set of all possible outcomes of
the experiment, denoted S.
An event is a subset of the sample space, denoted E.
Probability of event E (under an equally likely
assumption) is:
number of elements in E n( E )
P( E ) =
=
number of elements in S n( S )
My formula: P ( E ) =
# positive outcomes
total possible
Ex. An experiment consists of drawing one card
from a standard 52-card deck. What is the
probability of drawing:
1) A black card;
2) a red queen;
3) a six or club?
Ex. An experiment consists of rolling two fair dice
and adding the dots on the two sides facing up. Find
the probability of the sum of the dots indicated in
each part:
1)
Sum is 8;
2)
Sum is greater than 8;
3)
Sum is 13;
4)
Sum is not 2, 4 or 6.
The sample space of rolling two dice is:
Now we can update our formula:
# positive outcomes
P( E ) =
total possible
total possible−# negative outcomes
=
total possible
Ex. In a family with 3 children, excluding multiple
births, what is the probability of having 2 boys and
1 girl, in any order? Assume that a boy is as likely
as a girl at each birth.
Ex. In drawing 5 cards from a standard 52-card
deck without replacement, what is the probability
of getting 5 spades?
(0.005)