Transcript Slideshow

After completing this lesson you
will learn:
 To
find the probability of
independent events.
 To
find the probability of
dependent events.
Vocab with Review
Check your Skills
Lesson
Mini Quiz

Probability- the probability of an event, or
P(event), tells you how likely it is that
something will occur.

Outcome- is the result of a single trial, like one
roll of a number cube.

Sample Space-is all the possible outcomes.

Event- is any outcome or group of outcomes.
Theoretical Probability

When all possible
outcomes are equally
likely, you can find
theoretical probability
of an event using the
following formula:
P(event) = number of favorable outcomes
number of possible outcomes
Experimental Probability
• Probability based on data
collected from repeated
trials is experimental
probability, which is shown
in the following formula:
P(event) = number of times an event occurs
number of times the experiment is done
Next, click to see example of
Theoretical Probability & Experimental Probability


Next, click here to watch a video over,
Theoretical vs. Experimental Probability


Complement of an event: consists of all the
outcomes not in the event.
Odds- describes the likelihood of an event by
comparing favorable and unfavorable
outcomes.
Odds in favor of an event  number of favorable
outcomes to number of unfavorable outcomes
Odds against an event  number of unfavorable
outcomes to number of favorable outcomes
Next, click to see an example of Finding the Odds
Question: Find the odds in favor of the spinner
landing on a number greater than or equal to 6.
Solution:
Odds in favor of an event  number of favorable outcomes
to number of unfavorable outcomes

Favorable outcomes: 6,7,8

Unfavorable outcomes: 1,2,3,4,5
◦ (3 numbers)
◦ (5 numbers)
ANSWER: The odds are 3:5
Great job!
You have just completed
your 2.6 Vocab & Review!
Please click the button below to go back to
the main menu and start on Lesson 2.7.
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Before we get into the “nitty gritty” of
Probability of Compound Events you should
have already reviewed information from the
previous lesson. So let’s check your skills and
do a few questions. Please note, the questions
asked are skills needed in order to ‘move on’
and truly understand Probability of Compound
Events.
Please click on the button below to continue:
CHECK YOUR
SKILLS
For questions #1-2, please Find the probability
for one roll of a number cube.
1.P(multiples
a.½
b.1/6
c.1/3
d.5/6
of 3)
Yes, 1/3 is the probability of
rolling a multiple of 3.
Click to go to #2
PLEASE TRY AGAIN!
If a cube has numbers
1-6…Think, “what are the
multiples of 3 on that dice?”
TRY AGAIN!
Reminder, find the probability for one roll of a
number cube.
2. P(greater than 4)
a.
b.
c.
d.
1/6
2/3
1/3
5/6
Yes, 1/3 is the probability of rolling a
number greater than 4.
You are now done reviewing…click
below to start learning Lesson 2.7
Begin 2.7
PLEASE TRY AGAIN!
If a cube has numbers 1-6, how
many are greater than 4?
TRY AGAIN!
NEW VOCABULARY:


Independent events- are events that do not
influence one another.
Dependent events- are events that do
influence each other. The occurrence of one
event affects the probability of a second
event.
Rule:
Probability of Two Independent Events
If A & B are independent events,
 P(A and B)=P(A)*P(B).

Rule:
Probability of Two Dependent Events
If A & B are dependent events,
 P(A then B)= P(A)*P(B after A).

Next, click here to watch a video on
Independent Events & Dependent Events
Suppose you roll a red number cube and a
blue number cube. What is the probability that
you will roll a 3 on a red cube and even
number on a blue cube?
Solution:
P(red 3) =
(There is only one way to get a 3 out of six numbers)
P(blue even) = = (There are three even numbers out of six numbers)
P(red 3 and blue even) = P(red 3) * P(blue even)
=*=
ANSWER: The probability that you will roll a 3 on the red
number cube and even number on the blue cube is

Suppose you choose a tile at random from the
same letters in example 2: I, U, I, A, O, O, O, E, A, U,
A, O, A, E, E. Without replacing the tile, you select a
second tile. What is the probability that you will
choose an A and then an E?
◦ P(A) =
◦ P(E after A)=
◦ P(A then E) = P(A) *P(E after A)
=
ANSWER: The probability that you will choose an A and
then an E is
Nice job!
You are now done going over
Lesson 2.7…if you feel like you need to go back and
look through the examples again or take better
notes, feel free to head to the main menu and click
on Lesson 2.7 again or 2.6 if you feel necessary. If
not, you may begin your mini quiz over the two
sections. Good Luck!
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Mini Quiz
1. You take a three-question true false quiz. You
guess on all the questions. What is the probability
that you will get a perfect score?
a.
c.
b.
d.
You have a bag containing 3 green marbles,
4 red marbles, and 2 yellow marbles. You
select 1 marble randomly. What are the odds
against selecting green or yellow marble?
a. 5:4
b. 9:4
c. 4:9
d. 4:5
Suppose you select a two-digit number at random
from 10 to 30 (including 10 and 30).
Find P(number is a multiple of 6):
a.
11:21
b.
4:21
c.
1:5
d.
1:7

Click to go on
PLEASE TRY AGAIN!
You may want to be looking at your notes.
Hint: Look at your formula for Independent
Events.
TRY AGAIN!

Click to go on
PLEASE TRY AGAIN!
Make sure you make note that this
question is an example of
“selecting without replacement.”
TRY AGAIN!
Yes, the odds against are 4:5 of
the event.
Go to last question
PLEASE TRY AGAIN!
Remember…
Odds against an event  number of
unfavorable outcomes to number of favorable
outcomes.
TRY AGAIN!
GREAT JOB!!!
Yes, 4:21 is the probability of selecting a
number that is a multiple of
6…(12,18,24,30…4 numbers, out of a total of
21 possible numbers).
NEXT?
PLEASE TRY AGAIN!
Remember, the numbers can include 10 and
30. It may help to make a list that way you
have a visual.
TRY
AGAIN!
You are all done with your StAIR!!! I hope
you took good notes and have mastered your
learning of probability.

If for any reason, you want to go back and look
at things, feel free to head back to the main
menu.
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