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

May 18, 2012

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.

May 18, 2012

Probability Distribution: each outcome is assigned a unique probability

Outcome Probability

2

3

4

5

6

7

8

9

10

11

12

May 18, 2012

Find the probability of rolling a sum divisible by 2 on a single roll of two fair dice.

May 18, 2012

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 18, 2012

Is it possible to weight a standard 6-sided die in such a way that the probability of rolling each number n is exactly ? 1

(n2+1)

Outcome Probability1

2

3

4

5

6

May 18, 2012

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?

May 18, 2012

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 18, 2012

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?

May 18, 2012

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?

May 18, 2012

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(A and B) = P(A) P(B A)

P(chocolate chip jar B)

Conditional Probability Formula:

If the event B depends on the event A, then

P(B A) = P(A and B) P(A)

May 18, 2012

Given that the cookie chosen was chocolate chip, what is the probability that it came from jar A?

May 18, 2012

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

May 18, 2012

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?