Download 9.3 Probability Sample Space: possible results of an experiment

May 11, 2011
9.3 Probability
Sample Space: possible results of an experiment
Event: subset of the sample space
P(E) =
# outcomes in E
# outcomes in S
Find the sample space for each:
1. one coin is tossed
2. two coins are tossed
3. three coins are tossed
May 11, 2011
Find the probability of each event.
1. tossing a head on one toss of a fair coin
2. tossing two tails in a row on two tosses of a fair coin
3. drawing a spade from a standard deck of cards
4. rolling a four or five on one roll of a die.
5. rolling a sum of 4 on a single roll of two fair dice.
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Probability Distribution: each outcome is assigned a
unique probability
Outcome
2
3
4
5
6
7
8
9
10
11
12
Probability
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Find the probability of rolling a sum divisible by 2 on a single
roll of two fair dice.
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Probability Function: a fn P that assigns a real number to each
outcome in a sample space, S, subject to the following
conditions:
1. 0 < P(O) < 1 for every outcome O;
2. the sum of the probabilities of all outcomes in S is 1;
3. P(O) = 0
May 11, 2011
Is it possible to weight a standard 6-sided die in such a
way that the probability of rolling each number n is
1
exactly
?
(n2+1)
Outcome
1
2
3
4
5
6
Probability
May 11, 2011
Sal opens a box of two-dozen chocolate cremes and offers
three of them to Val. Val likes vanilla creme the best, but
all the chocolates look alike on the outside. If 11 of the 24
cremes are vanilla, what is the probability that all three of
Val's picks turn out to be vanilla?
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Multiplication Principle of Probability:
Suppose an event A has probability a and an event B has
probability b under the assumption that A occurs. Then
the probability that both A and B occur is ab.
May 11, 2011
Using a Venn Diagram
In a large high school, 43% of the students are girls and 45%
of the students play sports. Half of the girls at the school
play sports.
a. What percentage of the students who play sports are boys?
b. If a student is chosen at random, what is the probability
that it is a boy who does not play sports?