Math Tech IIII, Mar 28
Probability II – Computing Simple Probability
Book Sections: 3.1
Essential Questions: How can I compute the probability of any event?
What are the components of simple probability and how can I
compute it? What is the compliment of an event in a probability
computation?
Standards: PS.SPCR.2, PS.SPCR.7
Notation
• The probability of an event will be
abbreviated as follows:
P(event) =
The Mathematical Definition of Probability
Number of favorable outcomes
P(event) =
Total number of outcomes
In words: The probability of an event is the
ratio of favorable outcomes to the number
of possible outcomes. That number will
always be between 0 and 1. If 0, the event
is impossible, if 1, it is certain.
What is Simple Probability?
• Simple probability means one thing is
happening.
• It is the foundation of all probability.
What Are the Components of the Ratio
• Favorable outcomes – The number of ways within the sample space
that the event (what you want to occur) CAN occur
• Total number of outcomes – the number of things that can happen
in the sample space
• In these two counts you are counting the options, the outcomes are
not the options – it is the number of outcomes
The total number of outcomes is also known as all possible
outcomes
Ask This Question
• When computing probability, the question
is – How many are there? NOT What are
they?
Some Simple Examples
Favorable Outcomes (How Many?)
If you:
Select the number 5 on a roll of a die. = 1
Select an even number on a roll of a die. = 3
Select a red card from a deck of cards. = 26
Select a queen from a deck of cards. = 4
Select the 5 of diamonds from a deck of cards. = 1
Call heads on a coin flip. = 1
Some Simple Examples
Total Number of Outcomes
If you roll a single fair die, there are 6 possible outcomes, which are
1, 2, 3, 4, 5, 6 those are all the numbers on the standard cube
Drawing a single card from a deck. There are 52 possible outcomes,
because there are that many cards in the deck.
Flipping a coin has two possible outcomes, a head or a tail, there are
two sides on every coin.
Computing Probabilities
Selecting the number 5 on a roll of a die.
Selecting an even number on a roll of a die.
Selecting a red card from a deck of cards.
Selecting a queen from a deck of cards.
Selecting the 5 of diamonds from a deck of cards.
Calling heads on a coin flip.
Examples
P(4) =
P(red) =
P(even) =
P(odd) =
P(not 5) =
P(9) =
P(4 or 5) =
P(< 8) =
Examples
P(4) =
P(even) =
P(not 5) =
P(4 or 5) =
More Examples
P(odd)
P(green)
P(red)
P(17)
Examples
A bag contains 3 pink, 2 blue, 5 black, 1 clear and and
1 yellow marble. Compute the following probabilities
based on selecting a single marble from the bag:
P(black)
P(yellow)
P(green)
P(clear)
P(not blue)
P(yellow or blue)
Is It Really Random? Or Not
When is an occurrence random?
Answer: When every outcome is equally likely.
What About These?
Any problems here?
Complementary Events
The compliment of an event A is everything
happening except A
The compliment of A is called not A and is
abbreviated with A (called as A bar)
 Most of the time we will call it “not A”
Examples
The compliment of heads on a coin flip would be not heads which would be ‘tails’
The compliment of a 5 on a dice roll (not 5) - would be 1, 2, 3,
4, or 6
The compliment of a rainy day forecast for today - would be no
rain today
Complementary Events
An event will either happen or it will not.
All possible outcomes that are not an event add up to be the
compliment of that event.
The sum of the probability of an event and the event’s
compliment always add up to 1 or
P(event) + P(not the event) = 1, where P(not the event) is
the probability of the event’s compliment.
In Other Words
• The probability of a complimentary event is:
P(not event) = 1 – P(event) and
P(event) = 1 – P(not event)
Example: What is the probability of not getting a
3 when rolling a die?
1
1 5
– P(3) = 1  
6 6
Examples
Example
14
If P(tork) =
27
What is P(not tork)?
Class work: CW 3/28/17, Parts 1&2, All
Homework: None