Notes on Simple Probability

Opener for Probability Name______

What does it mean for an event to have a probability of ? If necessary, convert to a percentage in order to better understand its meaning.

One event has a probability of . Another event has a probability of . Which event is more likely to occur? How can one compare two probabilities to determine which is more likely?

Is it possible for an event to have a probability of ? How about ? How about ? What do you think is the highest probability that an event can have?

Fill in the blank based on the previous question: If the probability of an event is expressed as a fraction, then the numerator cannot be ______the denominator.

Do you think it is possible for an event to have a probability of ? Explain your reasoning.

In what jobs and in what areas of life is one likely to find probabliity?

In your own words, define probability.

The Makeup of the Standard 52-Card Deck

------

Possibilities When Rolling Two Six-Sided Dice

1 1 2 1 3 1 4 1 5 1 6 1

1 2 2 2 3 2 4 2 5 2 6 2

1 3 2 3 3 3 4 3 5 3 6 3

1 4 2 4 3 4 4 4 5 4 6 4

1 5 2 5 3 5 4 5 5 5 6 5

1 6 2 6 3 6 4 6 5 6 6 6

------

General Probability Help

Simple Probability - used when one total item is being chosen that can only come

from one group or category

ex. There are five gold tokens and four silver tokens in a bag. If one

is randomly selected, what is the probability it is gold?

OR Probability - used when one total item is being chosen that can come from

two or more groups or categories

95% of the time - the problem will contain the word "OR"

ex. There are five gold, four silver, and three bronze tokens in a bag. If one is randomly selected, what is the probability it is gold or silver?

AND Probability - used when two or more total items are being chosen

ex. There are five gold and four silver tokens in a bag. If three tokens are

drawn without replacing them, what is the probability that all are gold?

If there are more than two events, then each event assumes all of the

previous events were successful.

Notes on Simple Probability Name______

The probability of any event is the likelihood that the event will occur. In other words, when one is asking for the probability that something will happen, he/she is really asking, "How likely is it that something will happen?"

Probability =

***if every outcome has an equal chance of being selected***

If you look at the denominator of this formula, you will see "total outcomes". In the last unit, this is what we were obtaining. "Desired outcomes" is simply the number of ways in which you get what you want.

Probability =

------

Suppose that there are six gold tokens, four silver tokens, and ten bronze tokens in a bag. If one is randomly drawn, what is the probability that the token that is drawn is silver?

In this problem, each outcome (token) has an equal chance of being selected. Hence, the formula for probability at the top of this page can be used.

In the problem above, what do you want? How many ways can you get it (desired outcomes)?

What is the total number of possibilities (total outcomes)?

What is the probability that the token that is drawn is silver?

------

A box of baseball cards at Walmart contains sixteen packs of cards. If two of the packs contain Diamond Insert cards, what is the probability of selecting one pack that does not have a Diamond Insert card?

------

What fraction of the circle's area is occupied by the '1' space? This is the probability of spinning a '1' on the wheel?

What is the probability of spinning a '3'?

The probability of an event must be at least zero, and it can be no greater than one. Events with probabilities of zero are impossible. Events with probabilities of one are certainties (they will happen, for sure). For example, the probability that Mr. Middleton will give birth to a child in his lifetime is 0. The probability you will roll a number that is less than seven with a standard six-sided die is 1.

What is another event with a probability of zero?

What is another event with a probability of one?

------

Homework on Simple Probability

1. Joe is playing a game in which he is rolling a regular six-sided die. If Joe is able to roll a "2 or greater", he wins the game. What is the probability Joe wins the game?

2. There are sixteen girls and fourteen boys in a class. If one student is randomly selected

from the class, what is the probability that the student is a boy?

3. One card is drawn from a standard 52-card deck. See the diagram in the notes..

A)What is the probability that the card is a diamond?

B)What is the probability that the card is a numbered card?

C)What is the probability that the card is a face card (Aces are not face cards)?

D)What is the probability that the card is an Ace?

4. At Lakeside High School, suppose there are 600 freshmen, 500 sophomores, 450 juniors,

and 350 seniors. If a student is randomly chosen, what is the probability that the student

is a freshmen?

5. In the National League, there are five teams in the West, six teams in the Central, and

five teams in the East. What is the probability that a team from the East will win the

National League if each team has an equal chance to win?

------

Approve / Disapprove / No Opinion
Students / 2 / 57 / 1
Parents / 15 / 14 / 11

100 people were surveyed at a high school football game. They were asked the question, "Do you approve of having school year-round?" The results were placed in the table above.

9. What is the probability that a randomly surveyed person approves?

10. What is the probability that a randomly surveyed student disapproves?