Probability Day 1 - Understanding Probability Notes
Essential question: How can you describe the likelihood of an event?
Warm-up:
Discuss the following questions with your group. Record your answers here.
1)
How do you define probability?
2) Name some professions (jobs) that use probability.
3) What does it mean when you hear the weatherman predict a 10 percent chance of rain?
Is that a high or low probability?
Example 1 – Likelihood of an Event
When a six sided number cube is rolled once, the possible numbers that could show face up
are:
Each time you roll the cube, a number lands face up. This is called an event. Below is a list of
9 different events.
Work with a partner to order the events from those least likely to happen to the ones that are
most likely to happen when you roll the number cube one time. Use the space next to each
event to write any notes that might help you order them.
Rolling a number less than 7
Rolling an 8
Rolling a 1, 2, or 3
Rolling a 5
Rolling a number other than 6
Rolling an even number
Rolling a number greater than 5
Rolling an odd number
Rolling a prime number
Now answer the following questions:
1) How did you sort the events?
2) Are any of the events impossible? Why were they impossible?
An experiment is an activity involving chance in which results are observed. Each
observation of an experiment is a trial, and each result is an outcome. A set of one or more
outcomes is an event.
The probability of an event, written P(event), measures the likelihood that the event will
occur. Probability is a measure between 0 and 1 as shown on the number line and can be
written as a fraction, a decimal, or percent.
If the event is not likely to occur very many times, the probability of the event is close to 0.
Likewise, if an event is likely to occur many times, the event’s probability is closer to 1.
Example 2 – Describing Events
Determine whether each event is impossible, unlikely, as likely as not, likely, or certain.
Include the associated fraction, decimal and percent.
A) You flip a coin. The coin lands tails up.
B) You roll two number cubes and the sum of the numbers is 11.
C) A bowl contains 14 red marbles and 3 green marbles. You pick a red marble.
D) A spinner has 10 equal sections marked 1 through 10. You spin and land on a number
greater than 0.
E) Now You Try It!
Describe each event as impossible, unlikely, as likely as not, likely, or certain. Include the
associated fraction, decimal or percent.
1) A hat contains pieces of paper
marked with the numbers 1 through
20. You pick an even number.
2) A spinner has 8 equal sections
marked 1 through 8. You spin and
land on 0.
!
!
3) The probability of event A is !. The probability of event B is !. What can you conclude
about the two events?
The complement of an event is the set of all outcomes not included in the event. For
example, consider the event that you roll a number cube and get a 3. The complement is
the event that you do not roll a 3. The complement is rolling a 1, 2, 4, 5, or 6.
The sum of the probabilities of an event and its complement equals 1.
P(event) + P(complement) = 1
Example 3 – Using the Complement of an Event
Describe a standard deck of cards:
In a standard deck of cards, what is the probability of choosing a card at random and
getting an Queen? What is the probability of not getting an Queen?
P(Queen)=
P(event) + P(complement) =
P(Queen) + P (____________________________) = 1
____+ P(____________________________) = 1
P(not getting a Queen) = 1 - ____ =
Now You Try It!
1) A jar contains marbles marked with the numbers 1 through 10. The probability that you
!
pick a number at random and get a 5 is !".
A) What is the complement of this event?
B) What is the probability of the complement?
!
2) You roll a six-sided number cube. The probability that you roll an odd number is !.
A) What is the complement of this event?
B) What is the probability of the complement?
3) Why do the probability of an event and the probability of its complement add up to 1?
4) Give an example of a real-world event and its complement.