April 15, 2013
Basic Probability
In general, probability expresses the chances that something occurs. It
is often represented as a fraction or percentage.
Outcomes are the possible results of an action. An event is any outcome or group of outcomes.
When outcomes for an event are equally likely, you can use a ratio to find the
probability of an event.
number of favorable outcomes
P(event) =
number of possible outcomes
All probabilities range from 0 to 1. So,
an impossible event has a probability
of 0, and a certain event has a
probability of 1.
Theoretical Probability is simply the probability of an event occurring when each
outcome is equally likely.
April 15, 2013
Theoretical Probability is simply the probability of an event occurring when each
outcome is equally likely.
When tossing a fair die, what is the probability of getting heads?
If you roll a six-sided # cube, what is the probability of getting an odd #?
A number less than 6?
Not a 2 or 4?
April 15, 2013
Experimental Probability refers to the probability of an event
occurring when an experiment has been conducted.
number of event occurrances
Experimental Probability =
total number of trials
April 15, 2013
Determining Outcomes
A sample space is a list of all possible outcomes. A tree diagram
can be used to list possible combinations in a sample space.
Write the sample space for flipping two fair coins:
At the SMS school store, you can buy Raiders' shirts.
They have two colors (maroon and white), three sizes
(small, medium, large), and two fabrics (cotton, polyester).
Draw a tree-diagram to display the possible choices.
April 15, 2013
In the school cafeteria, they have the following choices for
sandwiches. White or wheat bread, ham or turkey, lettuce or
tomato, and mustard, mayonnaise, or barbeque sauce.
Use a tree diagram to list all the possible sandwich combinations.
The Counting Principle describes a way to calculate the total number of
choices when the ordering of the elements does not matter.
If there are m ways of making one choice, and n ways
of making a second choice, then there are (m)(n) ways
of making the first choice followed by the second.
April 15, 2013
April 15, 2013
Experimental Probability:
Replacement vs. Non-replacement A.K.A
Independent vs. Dependent Events
Independent events are events for which the occurrence
of one event does not affect the probability of the other.
For two independent events, A and B, the probability of
both events occurring is the product of each probability.
P(A, then B) = P(A) ⋄ P(B)
Examples: Rolling a number cube...
Find the probability of the following events:
1. P(even #, then a 2)
2. P(1, then # ≤ 4)
April 15, 2013
In some situations where the probability of an event can be calculated,
the likelihood of one event depends on how the experiment is conducted.
Most notable are situations where items are drawn and NOT REPLACED.
In these situations, not replacing an item
affects the probability of any future events.
Dependent events are events for which the occurrence of one
event affects the probability of the occurrence of the other.
For two dependent events A and B, the probability of both events occurring
is the product of the probability of the first, and the probability of the
second after the first has occurred.
P(A, then B) = P(A) ⋄ P(B after A)
Examples: There is a bag containing 10
colored squares. 5 Red, 2 Blue, 3 Green
April 15, 2013
Examples: There is a bag containing 10
colored squares. 5 Red, 2 Blue, 3 Green
April 15, 2013
Examples: In a standard deck of 52 playing cards (four suites, 3 face-cards/suite)...
Find the probability of the following events after drawing the first card, putting back
into the deck and then drawing the second.
1. P(spade, then spade)
2. P(face-card, then 5)
Examples: In a standard deck of 52 playing cards...
Find the probability of the following events after drawing the first card and notreplacing prior to the second draw.
1. P(spade, then spade)
2. P(face-card, then 5)