1. Probability of compound events
Today’s Lesson:
What:
Probability of compound events
Why:
. . . so I can create and analyze tree diagrams; discover and use the fundamental counting principle; and use multiplication to calculate compound probability.
How:
. . . by taking accurate notes, participating, and completing homework.

2. In your own words, explain how you calculate the probability of compound events?

3. Compound Probability involves MORE than one event!
Vocabulary:
Compound Probability- refers to probability of more than ____________ event.
Tree Diagram– shows the total possible __________________ of an event.
Fundamental Counting Principle– uses multiplication to determine the total possible outcomes when _________ than one event is combined.
Calculating Compound Probability– may use a tree diagram OR may _________________ the first event TIMES the second event.
one
outcomes
more
MULTIPLY

4. Tree Diagrams: Tossing Two Coins: Total Outcomes: _____ 4 Coin 2
Heads
Tails
Tails
Heads
Total Outcomes: _____ 4

5. Tossing Three Coins: Total Outcomes: _____ 8 H T H T H T H T Coin 3
Heads
_____
Tails H T H T
Tails
Heads
_____ H T H T
Total Outcomes: _____ 8

6. 3) Tossing One Coin and One Number Cube:
____ 1 2 3 H 4 5
____ 6 1 2 3 T 4 5 6
Total Outcomes: _____ 12

7. Chocolate or Vanilla Ice cream Sprinkles, Nuts, or Cherry
Choosing a Sundae with the following choices (may only choose one
from each category):
Chocolate or Vanilla Ice cream
Fudge or Caramel Sauce
Sprinkles, Nuts, or Cherry
Your turn to make a tree diagram . . .
Total Outcomes: _____ 12
Do we have to use a tree diagram? Is there a shortcut??

8. 3) Tossing one coin and one number cube:
Yes, there is The Fundamental counting principle !
We can multiply to determine the outcomes . . .
Tossing two coins:
Tossing three coins:
Multiply the outcomes for EACH event . . . 4 8
3) Tossing one coin and one number cube:
Spinning a spinner with eight equal regions, flipping two coins, and tossing one number cube: 12
192

9. 5) The total unique four-letter codes that can be created with the
following letter choices (each letter can be used more than
once)-- A, B, C, D, E, and F:
The total unique locker combinations for a four-digit locker
code (using the digits 0 – 9):
Choosing from 12 types of entrees, 6 types of side dishes, 8
types of beverages, and 5 types of desserts:
8) Rolling two number cubes:
1,296
10,000
2,880 36

10. 36,864 ways to “dress” a whataburger . . .
Fundamental counting principle in action . . .
How??
Think about it. The # of bread choices, times the # of meat choices, times the # of topping choices, times the # of sauce choices, etc., etc. It adds up fast!

11. Experimental Probability:
PROBABILITY TRIALS . . .
TRIAL #1: Rolling Two Number Cubes
Out of 20 trials, how many times will doubles occur– P(doubles)?
1) What do we need to know?
# of doubles:____
total # of outcomes: ___
Theoretical
Probability:
Do the experiment (20 trials): 4)
Experimental Probability: 6
(what should happen) 36
𝟔 𝟑𝟔 𝒐𝒓 𝟏 𝟔
(what actually happens)

12. Experimental Probability:
PROBABILITY TRIALS . . .
TRIAL #2 : Rolling a Number Cube and Flipping a Coin
Out of 20 trials, how many times will heads and a # less than 3 occur– P(heads and a # < 3)?
What do we need to know?
favorable outcomes: _____
total outcomes: _____
Theoretical
Probability:
Do the experiment (20 trials): 4)
Experimental Probability: 2
(what should happen) 12
𝟐 𝟏𝟐 𝒐𝒓 𝟏 𝟔
(what actually happens)

13. 𝟏 𝟐 x 𝟏 𝟐 = 𝟏 𝟒 Compound Probability sample questions:
When two coins are tossed, what is the probability of both coins landing on
heads – P (H and H) ?
We can draw a tree diagram to answer this.
OR, we can use MULTIPLICATION to solve:
𝟏 𝟐 x 𝟏 𝟐 = 𝟏 𝟒
P(1st Event ) x P(2nd Event)
2) When a number cube is rolled and the spinner shown is spun, what is the probability of landing on an even # and orange– P(even # and orange) ?
𝟑 𝟔 x
𝟏 𝟓 =
𝟑 𝟑𝟎 𝒐𝒓 𝟏 𝟏𝟎

14. a) P(ace and a vowel) b) P(red card and a “T”)
A card is drawn from a standard deck of cards and a letter is picked from a bag containing the letters M-A-T-H-E-M-A-T-I-C-S:
a) P(ace and a vowel) b) P(red card and a “T”)
𝟒 𝟏𝟒𝟑
𝟏 𝟏𝟏
A bag contains 3 grape, 4 orange, 6 cherry, and 2 chocolate tootsie pops. Once a pop is picked, it is placed back into the bag:
a) P(grape , then cherry)
b) P(two oranges in a row)
c) P(chocolate , then orange)
𝟐 𝟐𝟓
𝟏𝟔 𝟐𝟐𝟓
𝟖 𝟐𝟐𝟓

15. Wrap-it-Up/Summary:
In your own words, explain how you calculate compound probability.
Multiply the probability of the first event TIMES the probability of the second event!

16. END OF LESSON