MGF 1106 – Probability – Chapter 12

Section 12.1 – Empirical Probability - Read for Homework

Section 12.2 – Theoretical Probability - Vocabulary

Experiment – the activity taking place – EX: rolling dice, drawing cards, flipping

coins, etc.

Outcome - What might happen when an experiment takes place - Ex: rolling a three,

drawing an Ace of Hearts, tails on a coin, etc.

Sample space - the set of all possible outcomes

Event – A subset of the possible outcomes that contains the desired outcomes

Probability of an event -

P(E) = number of ways that event may occur

total number of all possible outcomes

Equally likely outcomes; No outcome is more likely to occur than any

other possible outcome.

The following are examples of some common “experiments” and events:

A. Roll one die

List the sample space:

Find each probability:

P(4) = P (not 4) = P(odd) =

P(7) = P(number less than 7) =

*** Notes:

When an event can never happen, P(event) = ______

When an event is guaranteed to happen, P(event) = ______

Probabilities always lie between ______and ______.

The sum of all possible probabilities = ______

P(not E) = ______


B. Outcomes that are NOT equally likely:

You are given a bag containing 5 quarters, 3 dimes, 2 pennies.

If you randomly select one coin from the bag, find

1. P(quarter) = ______

2. P(dime or penny) = ______

3. P(dime and penny) = ______

4. P(silver dollar) = ______

C. Spinners -

1. P( ) ______1. P( ) ______

2. P( ) ______2. P( )______

3. P( ) ______3. P( )______

4. P( or ) ______4. P( or ) ______

D. Charts -

Market research shows that the students at CJC have the

following preferences on type of carbonated beverage.

Regular Diet No

Cola Cola Cola

Freshmen 40 30 15

Sophomores 30 30 20

If a random CJC student is selected, determine the probability

that the student fits the following category.

1. P(freshman and diet) = ______2. P(regular cola) = ______

3. P(Sophomore) = ______4. P(Not diet) = ______


E. Percents – "PER HUNDRED"

A study of the investment market shows that 40% of the population invests in stocks,

30% invests in bonds, 12% invests in savings accounts, and the remainder do not invest.

If a citizen is selected at random, find probability that the citizen invests in"

1. P(stocks) = ______2. P(bonds or savings) = ______

3. P(not stocks) = ______4. P(not investing) = ______

F. From a deck of cards: (See below for details)

Experiment: Draw a single card from a normal card deck.

Find probability of drawing:

1. P(A) = _____ 2. P(A hearts) = _____

3. P(Face card) = _____ 4. P(odd) = _____

5. P(King or Queen) = _____ 6. P(King and Queen) = _____

7. P(King and diamond) = _____

A standard deck of 52 cards (no jokers) contains the following:

52 Cards
26 Red / 26 Black
13 Diamonds / 13 Hearts / 13 Clubs / 13 Spades
King

Queen

Jack
10
9
8
7
6
5
4
3
2
Ace / King
Queen
Jack
10
9
8
7
6
5
4
3
2
Ace / King
Queen
Jack
10
9
8
7
6
5
4
3
2
Ace /

King

Queen
Jack
10
9
8
7
6
5
4
3
2
Ace

HW: pg 588 4, 13 – 30 all, 39 – 48 all, 57 – 68 all

(041)