Download 9.3 Probability Sample Space: possible results of an experiment

May 18, 2012
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
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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
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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
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Sal opens a box of two-dozen chocolates filled with vanilla
or chocolate creme. He 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.
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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?
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Two identical cookie jars are on a counter. Jar A contains 2
chocolate chip and 2 peanut butter cookies, while jar B
contains 1 chocolate chip cookie. We select a cookie at
random. What is the probability that it is a chocolate chip
cookie?
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Conditional Probability:
ex. the cookie was dependent on the jar outcome
P(A B): P of A given B
P(A B) = P( A and B)
P(B)
Cookie Example:
P(chocolate chip jar A)
P(chocolate chip jar B)
P(A and B) = P(A) P(B A)
Conditional Probability Formula:
If the event B depends on the event A, then
P(A and B)
P(B A) =
P(A)
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Given that the cookie chosen was chocolate chip, what
is the probability that it came from jar A?
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Binomial Distributions
We roll a fair die four times. Find the probability that
we roll:
a. all 5's
b. no 5's
c. exactly three 5's
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Suppose Mike makes 90% of his free throws. If he shoots
20 free throws, and if his chance of making each one is
independent of the other shots, what is the probability
that he makes:
a. all 20?
b. exactly 18?
c. at least 18?