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Probability
Probability is the chance that something will happen. In other words, how likely that some event will
happen.
We see probability every day in our life. You may not realize that what you are looking at deals with
probability. For example, when you watch the weather report on the news and the meteorologist tells
you that there is a 40% chance of rain on a particular day – that is an example of probability. When you
watch many games shows such as Deal or No Deal, The Price is Right, or Wheel of Fortune we may not
notice it, but there are concepts tied to probability in those games.
Let’s say you have 1 6-sided dice and you rolled the dice once. What is the probability that the dice will
land on a 3?
To find the probability that a certain event happens –
We can represent the probability of events in three different ways
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

The probability that an event will happen will range between the values _____ and ______.


The sample space is a listing of all possible outcomes.
If we took the letters in the word PROBABILITY, what would the sample space be?
Sometimes, writing down the sample space is very tedious. For example, if I asked you to write down the
sample space for drawing a card out of a standard deck of 52 cards, you would have to write 52 things
down.
On the back of this page, I have included a picture that shows the samples space for choosing a card from
a standard deck of cards.
For the questions below refer to the picture above(if needed). Be very careful. Some questions are
tricky.
You pull 1 card randomly from a standard deck of cards. Find the probability of the following events. If
you leave your answer as a fraction, make sure that the fraction is reduced to lowest terms.
1.
2.
3.
4.
5.
6.
7.
8.
9.
P(heart)
P(jack)
P(red)
P(face card)
P(3 of hearts)
P(spade or 10)
P(ace and king)
P(black or 6)
P(black or red)
Answers:
1.
2.
3.
4.
6.
7.
8.
9.
5.
Now let’s take a look at the poker chips that I have given your table.
1. How many poker chips do you have? ________
2. How many of each color do you have? Red _____ Black _____
Blue _____
Green _____
3. Let’s say that these poker chips are put in a bag and you draw a chip at random. Leave your
answer as a fraction.
P(Red) =
P(Black) =
P(Green) =
What do you notice if you add the probabilities together?
P(Blue) =
Rule 1: The sum of the probability of all outcomes is always ______.
Suppose you have a bag of red and green marbles, but you do not know how many marbles are in the bag
or the number of each color. However you are told P(red marble) = ¼.
How could we figure out P(green marble) without touching the bag of marbles?
Rule 2: If P(A) = x, then P(not A) = ________________________. In math instead of writing P(not A), we will
use the notation P(A’). These events are called _________________________.
Right now, rule 2 may not be very useful for us, but it will become useful when we start doing compound
events.
Compound Events
When we look at the probabilities of the outcomes of rolling a 1 dice, choosing one marble out of a bag,
spinning a roulette wheel once, etc., that is finding the probability of a single event.
If we roll 2 or more dice, flip 2 or more coins, pull 2 or more marbles out of a bag, etc., it is called
compound events.
The game of SKUNK is also an example of compound events.
Most of the time, it is very beneficial to draw a diagram to help us calculate the probabilities of compound
events. We used a table to help us calculate the probabilities of certain events happening in SKUNK.
We can use a table when there are only 2 events occurring. On one side we list the outcomes of 1 event
and we list the other set of outcomes across the top. Then depending on what the question asked, we
filled in the table.
Example: You flip a coin and roll a 6-sided dice. Create a table that will help determine the probability of
different events.
Use the table above to find the answers to the questions below:
1.
2.
3.
4.
5.
P(the coin lands on heads)
P(the number 4 is rolled on the dice)
P(Heads & 4)
P(Heads or 4)
P(Tail & Odd Number)
Answers
1.
2.
3.
4.
5.
Example: 2 4 – sided dice are rolled and the PRODUCT of the two numbers shown is written down.
Create a table that will help determine the probability of different events.
Use the table above to help you answer the questions below:
1.
2.
3.
4.
5.
P(product = 2)
P(product is a perfect square)
P(product > 8)
P(product = 15)
P(product is odd)
Answers:
1.
2.
3.
4.
5.
Without using the table that you create above, explain how you could find P( product  8) .
Example: 2 spinners are spun simultaneously. One of the spinners only has 3 regions with the colors red,
blue, and orange. The other spinner has 4 regions whose colors are blue, green, yellow, and orange.
Create a table that shows all possible outcomes for spinning these two spinners.
Use the table above to answer the following questions:
1. P(same color)
2. P(2 primary colors)
Without looking at the table, explain how you can find P(different colors)?
Can you use this method to find P(2 secondary colors)? Why or why not?