NOTES 3.9 – THEORETICAL PROBABILITY – DAY 1

Each time an experiment such as one toss of a coin, one roll of a dice, one spin on a spinner etc.

is performed, the result is called an ___________.

Theoretical Probability is a measure of what you ________ to occur.

A _______________ for an experiment is the set of possible outcomes for that experiment.

OUTCOME

EXPECT

SAMPLE SPACE

Example 1:

Create a sample space for the following situation: Mr. And Mrs. Sanderson are expecting triplets. Assume there is an equally likely chance that the Sandersons will have a boy or girl.

 

 

Total Number of Outcomes:

B B B G B B

B G B

B B G

G G B

G B G

B G G

G G G

8

Theoretical Probability =

Number of FAVORABLE outcomes in the sample space

Number of TOTAL outcomes in the sample space

 

Notation: The probability of a certain event occurring is notated by _____.

Where P stands for _________ and E is the ______ occurring.

( )P E FAVORABLETOTAL

( )P E

probability event

Example 2 - Using the sample space above, if the couple has 3 children, what is the probability of having 2 boys and 1 girl?

P( of 2 boys) = P( of 3 girls) =

 

P( of 1 boys) = P( of 2 girls) =

38

18

38

38

Example 3 - Out of 100 families with 3 children how many would you expect to have all girls?

P( of 3 girls) =

 

18 100

n

18

8 100n

12.5n

8 100

8 8

n

or about 13 families

The above situation is an example of an ______________ event because the outcome of one event does not affect the probability of the other events occurring.

Example 4 - Radcliff is playing a game where he

spins the spinner below and tosses

and coin right after. Create a sample

space for all possible outcomes, and

then answer the questions below.

INDEPENDENT EVENTS:

1 2

4 3

INDEPENDENT

Spinner

Coin

 

 

1 1 2 2 3 3 4 4H H H HT T T T

P(1)? P(Tails)?

P(1 and Tails)? P(Even and Heads)?_______

P(5 and Tails)? P(Odd or Heads)?

2 18 4

4 18 2

18

2 18 4

0 08

6 38 4

Mathematically-

AND means we can MULTIPLY each individual probability.

OR means we can ADD the probabilities. (But don’t count an event twice!)

  P(Even and Heads) = P(E) x P(H) =

= 1

2

1

2

1

4

  P(Odd or Heads) = P(O) + P(H) - P(O and H) =

HW : Section 3.9 pages 193-194 #’s 6-29

1

2

1

2

1

4

- = 3

4

NOTES 3.9 – THEORETICAL PROBABILITY – DAY 2

Some probability events require the act of ____________ an item back before choosing another item. These events are called events _____________________.

Other probability events require the act of _________________ an item before choosing another item. These events are called events ___________ _______________.

WITH OR WITHOUT REPLACEMENT

REPLACING

WITH REPLACEMENT

NOT REPLACINGWITHOUT

REPLACEMENT

Example 1 - Suppose a bag contains 12 marbles: 6 red (R), 4 Green (G), and 2 yellow (Y). Two marbles are randomly drawn. Use a grid to find the following probabilities:

First marble returned

(independent event)

First marble not returned (dependent event)

P(R, then R)

P(R, then G)

P(R, then Y)

P(G, then R)

P(G, then G)

P(G, then Y)

6 6

12 12

1 1

2 2

6 5

12 11

1 5

2 11

6 4

12 12

1 1

2 3

6 4

12 11

1 4

2 11

6 2

12 12

1 1

2 6

6 2

12 11

1 2

2 11

4 6

12 12

1 1

3 2

4 6

12 11

1 6

3 11

4 4

12 12

1 1

3 3

4 3

12 11

1 3

3 11

4 2

12 12

1 1

3 6

4 2

12 11

1 2

3 11

1

4

5

221

6

2

111

12

1

111

6

2

111

9

1

111

18

2

33

First marble returned

(independent event)

First marble not returned (dependent event)

P(Y, then R)

P(Y, then G)

P(Y, then Y)

2 6

12 12

1 1

6 2

2 6

12 11

1 6

6 11

2 4

12 12

1 1

6 3

2 4

12 11

1 4

6 11

2 2

12 12

1 1

6 6

2 1

12 11

1 1

6 11

1

12

1

11

1

18

2

331

36

1

66

CARDS

A standard deck of playing cards consist of ___ cards.

There are __ colors; RED and BLACK. ____ of each.

There are __ suits; HEARTS, DIAMONDS, CLUBS, and SPADES.

____ of each.

Each suit consist of the cards 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. 

__ of each.

52

2 26

4

13

4

Example 2 - Suppose you are going to pull two cards from a standard deck of 52, one right after the other WITHOUT replacing the first card. Find the following probabilities:

1.) P(A red and then a black) =

 

2.) P(Spade and then a Heart) =

=26 26

52 51

13

51

=13 13

52 51

13

204

3.) P(Jack and then an ACE) =

 

4.) P(2 Reds) =

5.) P(2 Kings) =

HW : Section 3.9 pages 193-194 #’s 30-45

=4 4

52 51

4

663

=26 25

52 51

25

102

=4 3

52 51

1

221