Today’s Lesson:
. . . so I can create and analyze tree diagrams; discover and use
the fundamental counting principle; and use multiplication to
calculate compound probability.
. . . by taking accurate notes, participating, and completing
homework.
In your own words, explain
how you calculate the
probability of compound
events?
Compound Probability involves MORE than one event!
Vocabulary:
Compound Probability- refers to probability of more than
____________
event.
one
outcomes
Tree Diagram– shows the total possible __________________
of
an event.
Fundamental Counting Principle– uses multiplication to
determine the total possible outcomes when _________
more than
one event is combined.
Calculating Compound Probability– may use a tree diagram
OR may _________________
the first event TIMES the second
MULTIPLY
event.
Tree Diagrams:
1)Tossing Two Coins:
Coin 1
Coin 2
Heads
Heads
Tails
Heads
Tails
Tails
4
Total Outcomes: _____
2)Tossing Three Coins:
Coin
1
Coin
2
Heads
Heads
Tails
Heads
Tails
Tails
Coin
3
H
_____
_____
T
H
_____
_____
T
_____
H
_____
T
H
_____
T
_____
Total Outcomes: _____
8
3)
Tossing One Coin and One Number Cube:
Coin
Number
Cube
1
____
2
____
____
H
3
____
____
4
____
5
____
6
____
1
2
____
T
____
3
____
____
4
____
5
____
6
12
Total Outcomes: _____
4) Choosing a Sundae with the following choices (may only choose one
from each category):
Chocolate or Vanilla Ice cream
Your turn to
Fudge or Caramel Sauce
make a tree
diagram . . .
Sprinkles, Nuts, or Cherry
12
Total Outcomes: _____
Do we have to use a tree diagram? Is there a shortcut??
We can multiply to determine the outcomes . . .
1)Tossing two coins:
Multiply the
outcomes for
EACH event . .
.
4
2)Tossing three coins:
8
3) Tossing one coin and one number cube:
12
4) Spinning a spinner with eight equal regions, flipping two
coins, and tossing one number cube:
192
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:
1,296
6) The total unique locker combinations for a four-digit locker
code (using the digits 0 – 9):
10,000
7) Choosing from 12 types of entrees, 6 types of side dishes, 8
types of beverages, and 5 types of desserts:
2,880
8) Rolling two number cubes:
36
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!
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?
2)
Theoretical
Probability:
6
# of doubles:____
(what should happen)
total # of outcomes: 36
___
3) Do the experiment (20 trials):
𝟔
𝟏
𝒐𝒓
𝟑𝟔
𝟔
4)
Experimental Probability:
(what actually happens)
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)?
1) What do we need to know?
2)
Theoretical
Probability:
2
favorable outcomes: _____
(what should happen)
12
total outcomes: _____
3) Do the experiment (20 trials):
𝟐
𝟏
𝒐𝒓
𝟏𝟐
𝟔
4)
Experimental Probability:
(what actually happens)
1)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 𝟏
x =
𝟔 𝟓
𝟑
𝟏
𝒐𝒓
𝟑𝟎
𝟏𝟎
3) 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
4)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)
𝟐
𝟐𝟓
b) P(two oranges in a row)
𝟏𝟔
𝟐𝟐𝟓
c) P(chocolate , then orange)
𝟖
𝟐𝟐𝟓
Wrap-it-Up/Summary:
1) In your own words, explain how you calculate compound
probability.
the probability of the first event TIMES the
probability of the second event!
END OF LESSON