Objectives:
Students will be able to find the probability of a
simple event.
Students will be able to understand the
distinction between simple events and compound events.
Essential Question:
(1) How do I find the probability of a simple event? (2) How can I distinguish between a simple and compound event?
Standards:
7.SP.5, 7.SP.6, 7.SP,7, 7.SP.8
VOCABULARY
Experiment – an investigation that has varying
results
Outcomes – all the possible results of an experiment
Event – a collection of one or more outcomes
Favorable outcomes – the specific event which you
want/expect to happen
Simple Events – consist of only one event
Compound Events – consists of more than two
events
Independent Events – the occurrence of one event
does not affect the likelihood that other event will occur
Dependent Events – the occurrence of one event
PROBABILITY
Probability is
a measure of how likely an
event is to occur
(or the chance that
something will happen
It is the ratio of the number of ways a certain
event can occur to the number of possible
outcomes
Formula –
number of favorable outcomes
number of possible outcomes
For example –
Today there is a 60% chance of rain.
The odds of winning the lottery are a
million to one.
Rolling dice
Spinner
Flipping a coin
Pulling a card out of a deck
What are some examples you can think
of?
DESCRIBING
PROBABILITY
You can describe the probability of an event with the following terms:
Certain – the event is definitely going to happen
Likely – the event will probably happen
Unlikely – the event will probably not happen,
but it might
Impossible – the event is definitely not going to
PROBABILITY
If an event is
certain
to happen, then the
probability of the event is 1 or 100%.
If an event will
NEVER
happen, then the
probability of the event is 0 or 0%.
If an event is
just as likely
to happen as
HOW LIKELY?
0% 25% 50% 75% 100%
0 ¼ or 0.25 ½ or 0.5 ¾ or 0.75 1
Impossible Unlikely Equally
When a meteorologist states that the chance of
rain is 50%, the meteorologist is saying that it is
equally likely to rain or not to rain.
If the chance of rain rises to 80%, it is more
likely to rain.
If the chance drops to 20%, then it may rain, but
it probably will not rain.
YOUR TURN
What are some events that will never
happen and have a probability of 0%?
What are some events that are certain to
happen and have a probability of 100%?
What are some events that have equal
WHAT ARE
OUTCOMES?
P(event) = number of
favorable
outcomes
total # of
possible
outcomes
An
outcome
is all the possible results of a
probability experiment
FAVORABLE
OUTCOMES
P(event) = number of
favorable
outcomes
total # of
possible
outcomes
An
favorable outcome
is the outcome (or
event) you want to happen in the
experiment.
When rolling a number cube, the event of rolling an even number is 3 (you could roll a 2, 4 or 6). So if you want to roll an even
EXAMPLE
P(event) = number of
favorable
outcomes
total # of
possible
outcomes
What is the probability of getting heads
when flipping a coin?
P(heads) = number of ways = 1 head on a coin = 1 total outcomes = 2 sides to a coin = 2
GUIDED
PRACTICE:
Calculate the probability of each simple
event.
1) P(black) =
2) P(1) =
3) P(odd) =
GUIDED PRACTICE -
ANSWERS
Answers
1) P(black) =
4/8 or ½, 0.5, 50%
2) P(1) =
1/8, 0.125, or 12.5%
3) P(odd) =
½, 0.5, 50%
1. What is the probability that the spinner will stop on part A?
3. What is the probability that the spinner will stop on
(a) An even number? (b) An odd number?
4. What is the probability that the spinner will stop in the area
marked A? A B C D 3 1 2 A C B
TRY THESE:
1. What is the probability that the spinner will stop on part A? ¼ or 25%
2. What is the probability that the spinner will stop on
(a) An even number? 1/3, 0.3, or 33.3%
(b) An odd number? 2/3, 0.6, or 66.7%
3. What is the probability that the spinner will stop in the area
marked A? 1/3, 0.3, or 33.3%
A B C D 3 1 2 A C B
ANSWERS:
PROBABILITY WORD
PROBLEM:
Lawrence is the captain of his track team. The
team is deciding on a color and all eight members wrote their choice down on equal size cards. If Lawrence picks one card at random, what is the probability that he will pick blue?
Number of blues = 3 Total cards = 8
yellow red blue blue blue green black black
Donald is rolling a number cube labeled 1 to 6.
What is the probability of the following? a.) an odd number
odd numbers – 1, 3, 5
total numbers – 1, 2, 3, 4, 5, 6
b.) a number greater than 5 numbers greater – 6
total numbers – 1, 2, 3, 4, 5, 6
LET’S WORK THESE
TOGETHER
3/6 = ½ = 0.5 = 50%
1. What is the probability of spinning a number greater than 1?
2. What is the probability that a spinner with five congruent sections numbered 1-5 will stop on an even number?
3. What is the probability of rolling a multiple of 2 with one toss of a number cube?
TRY THESE:
2 1
1. What is the probability of spinning a number greater than 1? ¾, 0.75, or 75%
2. What is the probability that a spinner with five congruent sections numbered 1-5 will stop on an even number? 2/3, 0.6, or 66.7%
3. What is the probability of rolling a even # with one toss of a number cube?
3/6 or ½ , 0.5, or 50%
ANSWERS:
2 1
COMPOUND EVENTS
All of the previous examples where simple events (only
one event was occurring).
Compound events consist of two or more events
occurring together.
When you have compound events you should consider if
the events are happening at the same time or one after the other.
Compound events can be either independent or
dependent
With independent events the occurrence of one event
does not affect the likelihood that the other event(s) will occur.
With dependent events the occurrence of one event
Independent – the chance of one event does not
affect the chance of the 2nd event.
Examples:
Flipping a coin & rolling a dice It rained today & my chair broke
When calculating independent events you multiply
the probabilities
Dependent – the change of one event does affect
the chance of the 2nd event.
Examples
Pulling a name stick from the jar & not returning the stick
when you pull a 2nd stick. Each time you pull a name the
chances become greater.
INDEPENDENT VS.
DEPENDENT?
Determine if the events are dependent or independent.
A.Getting tails on a coin toss and rolling a 6 on
a number cube
B.Getting 2 red gumballs out of a gumball
machine
C.Rolling a 6 two times in a row with the same
dice
D.A computer randomly generating two of the
ANSWERS
A. Getting tails on a coin toss and rolling a 6 on a
number cube
Tossing a coin does not affect rolling a number cube, so
the two events are independent.
B. Getting 2 red gumballs out of a gumball machine
After getting one red gumball out of a gumball machine,
the chances for getting the second red gumball have changed, so the two events are dependent.
C. Rolling a 6 two times in a row with the same dice A. The first roll of the number cube does not affect the
second roll, so the events are independent
D. A computer randomly generating two of the same
number
The first randomly generated number does not affect the
FIND THE PROBABILITY
P(jack, factor of 12)
1
5
5
8
x =
5
40
1
8
Independent Events
FIND THE PROBABILITY
P(Q, Q)
All the letters of the
alphabet are in the
bag 1 time
Do not replace the
If two events are happing at the same time,
you need to multiply the two probabilities together.
Usually the questions use the word “and” when
describing these outcomes.
Examples:
Tossing two dice and getting a 6 on both of them
Drawing a red and blue marble from a bag.
Pick a card, get an Ace and a red.
OCCURRING TOGETHER
EXAMPLE
If two events are happening one after the other,
you need to add the probabilities.
Usually the questions use the word “or” when
describing these outcomes.
Examples:
In a bag of marbles, pulling a red or blue
With a deck of cards, drawing an Ace or King
While pulling class sticks, drawing a boy or girl.
