Probability
Teacher
Probability
Data Analysis and Probability:
Students will understand how to formulate questions, analyze data, and determine
probabilities.
D.4 Understand and apply basic concepts of probability.
5.D.4.2 Describe and predict the results of a probability experiment.
5.D.4.5 Use fractions to describe the results of an experiment.
When teaching probability, follow these steps: Count the total possible outcomes (this
will be your denominator) and then count the total number of possibilities (this will be
your numerator). Example: If you have 20 total marbles and 4 of the marbles are red then
you will have a 4 in 20 chance of getting a red marble. The answer can be represented in
different ways.
(4/20) or (4 out of 20) or (4 in 20)
Remember, find the total possible outcomes and then find the possibility of what you are
looking for.
Theoretical probability-in theory what is the outcome.
number of favorable outcomes/total number of possible outcomes
Experimental probability-what occurs when you conduct an experiment.
number of times an event occurs/number of experiment
Another concept the students must know is the words or descriptions of an outcome.
They are:
Certain = There is a 100% chance of it happening. Example: There are 20 red marbles in
a bag. What are the odds of reaching in and getting a red marble? 20/20, there is no other
possibility.
Likely = There is a better than 50-50 chance of it happening but is not certain.
Example: There are 10 marbles in a bag and 9 of them are red. What is the chance of
getting a red marble? 9/10, this is better than half or more than half so it is likely that it
will happen.
Even Chance = There is a 50-50 chance of it happening. This is like flipping a coin, there
are only two choices, heads or tails. There is an even chance of getting heads or tails.
Unlikely = There is a les than 50-50 chance of it happening, but not impossible.
Example: There are 5 marbles in a bag, 4 are yellow and 1 is green. The odds of getting a
green marble is 1 out of 5. This is less than a 50-50 chance but not impossible, so it is
unlikely to get a green marble.
Impossible = There is absolutely no chance of the desired result happening. Example:
There are 100 marbles in a bag, what are the odds of getting a cube out of the bag? 0/100,
no chance at all. So this will be impossible.
Compound events=consists of two or more events. Two events are independent events
if the occurrence of one event does not affect the probability of the occurrence of the
other. Ex. Two spinners, what happens on one, does not affect what happens on the other.
Dependent events do affect the probability of the occurrence of the other. Ex. A deck of
cards, if you draw one and do not put it back it affects what can be drawn on the second
draw.
If an event wants this outcome or that outcome, you add them together. If the event wants
this then that, you multiply.
Teacher
Samples
Debbie has two fair spinners like the ones above. If Debbie spins each spinner once, what
is the probability that one arrow will land on and odd number, and the other arrow will
land on the letter G?
Using the same two spinners, what is the probability of Debbie getting the number 20 and
a Z?
Student Practice
1.
2.
In a class of girls and boys and using the spinner above, what is the probability of
a boy getting a free assignment?
3. There are 7 red gumballs, 5 green gumballs, 3 yellow gumballs, 4 blue, and 1
orange gumballs. What is the probability of getting a yellow gumball and not
getting a blue?