Transcript Calculating Compound Probability

Today’s Lesson:
What:
probability of compound events
Why:
To create and analyze tree diagrams;
discover and use the fundamental counting
principle; and use multiplication to
calculate compound probability.
Compound Probability involves MORE
than one event!
Vocabulary:
Compound Probability- refers to probability of
one
more than ____________
event.
Tree Diagram– shows the total possible
outcomes
__________________
of an event.
multiplication
Fundamental Counting Principle– uses ____________
to determine the total possible outcomes when
more than one event is combined.
Calculating Compound Probability– may use a
MULTIPLY the first
tree diagram OR may _________________
event TIMES the second 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
Fudge or Caramel Sauce
Sprinkles, Nuts, or Cherry
Your turn to
make a tree
diagram . . .
Do we have to use a tree diagram?
Is there a shortcut??
12
Total Outcomes: _____
We can multiply to determine the outcomes . . .
Multiply the
outcomes for
EACH event . .
.
1) Tossing two coins:
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:
# of doubles:____
6
36
total # of outcomes: ___
3) Do the experiment (20
trials):
(what should happen)
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)
favorable outcomes: _____
2
Theoretical
Probability:
(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) ?
𝟏
𝟑
𝟏
𝟑
x
𝒐𝒓
=
𝟓
𝟑𝟎
𝟏𝟎
𝟔
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
END OF LESSON
The next slides are student copies of the notes for this
lesson. These notes were handed out in class and
filled-in as the lesson progressed.
NOTE: The last slide(s) in any lesson slideshow
(entitled “Practice Work”) represent the homework
assigned for that day.
NAME:
What:
Math-7 NOTES
DATE: ______/_______/_______
probability of compound events
Why: To create and analyze tree diagrams; discover and use the fundamental
counting principle; and use multiplication to calculate compound probability.
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– used 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.
Tree Diagrams:
1) Tossing Two Coins:
Coin 1
Heads
Tails
Coin 2
Heads
Tails
Heads
Tails
Total Outcomes: _____
2) Tossing Three Coins:
Coin
1
Coin
2
Heads
Heads
Tails
Heads
Tails
Tails
Coin
3
_____
_____
_____
_____
_____
_____
_____
_____
Total Outcomes: _____
3) Tossing One Coin and One Number Cube:
Coin
Number
Cube
____
____
____
____
____
____
____
____
____
____
____
____
____
____
Total Outcomes: _____
4) 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
Total Outcomes: _____
Is there a shortcut?
We can multiply to determine the outcomes . . .
NAME:_____________________________________________________________________________
DATE: ______/_______/_______
“probability of compound events”
Coin 1
Coin 2
Coin 3
Coin 4
Child 1
Child 2
Child 3
Child 4
NAME:_____________________________________________________________________________
DATE: ______/_______/_______
“probability of compound events”
𝟏
𝟔
𝟏
𝟗
𝟏
𝟏
𝟔
𝟑𝟔
x =
𝟏
𝟏
𝟓
𝟒𝟓
x =