Name:_________________________________
M5L5
Date:_________
Accordino-Math 7
Period:________
Lesson 5: Using Tree Diagrams to Represent a
Sample Space and to Calculate Probabilities
Bellringer
Use the following information below to answer the two following questions:
Students are playing a game that requires spinning the two spinners shown below.
Red
Red
Blue
Green
1. Which of the following represents the sample space for this game?
a.
{RR,RB,RY,RG,BB,BY,BG,BR}
b.
{RB, RBYG}
c.
{RB,RY,RG,BY,BG,BR}
d.
{2,4}
2. Which of the following represents the probability of spinning two reds?
a. 0.5
b. 0.25
c. 0.125
d. 0.75
Blue
Yellow
Name:_________________________________
M5L5
Date:_________
Accordino-Math 7
Period:________
Lesson 5: Using Tree Diagrams to Represent a Sample Space
and to Calculate Probabilities
Notes
Example 1:
Students are playing a game that requires spinning the two spinners shown below. List the sample space of
possible outcomes below:
Blue
Red
Red
Blue
Green
Yellow
Instead of just listing the outcomes we can also create a Tree Diagram that outlines how each action connects to
the next, eventually creating a single “event” that we can find the probability of.
a.
What is the probability of
spinning two reds?
b.
What is the probability of
spinning a different color on
both spins?
c.
What is the probability of not
spinning green.
Name:_________________________________
M5L5
Accordino-Math 7
Date:_________
Period:________
Example 2:
Draw a tree diagram outlining the outcomes of flipping a coin twice?
What is the probability of getting a heads on the first flip and a tails on the second?
Example 2:
Imagine that a family decides to play a game each night. They all agree to use a tetrahedral die
(located at right) each night to randomly determine if they will play a board game (B) or a card
game (C). The tree diagram mapping the possible overall outcomes over two consecutive nights
will be developed below.
To make a tree diagram, first present all possibilities for the first stage. (In this case, Monday.)
Monday
Tuesday
Outcome
B
C
a.
If BB represents two straight nights of board games, what does CB represent?
b.
List the outcomes where exactly one board game is played over two days. How many outcomes were
there?
Name:_________________________________
Accordino-Math 7
M5L5
Date:_________
Period:________
Homework:
1) Which tree diagram shows all of the possible outcomes for tossing a coin and rolling a fair number
pyramid that has four sides labeled 1 through 4?
2) An owner of a small store knows that in the last week, 44 customers paid with cash, 13 paid with a debit
card, and 143 paid with a credit card. Which below is closest to the probability of a person paying with a
debit card?
a.
0.13
b.
0.075
c.
0.75
d.
0.78
Name:_________________________________
M5L5
Accordino-Math 7
Date:_________
Period:________
3) Imagine that a family of three (Alice, Bill, and Chester) plays bingo at home every night. Each night, the
1
chance that any one of the three players will win is .
3
a.
Using A for Alice wins, B for Bill wins, and C for Chester wins, develop a tree diagram that shows
the nine possible outcomes for two consecutive nights of play.
b.
Is the probability that “Bill wins both nights" the same as the probability that “Alice wins the first
night and Chester wins the second night”? Explain.
4) In a laboratory experiment, two mice will be placed in a simple maze with one decision point where a
mouse can turn either left (L) or right (R). When the first mouse arrives at the decision point, the
direction it chooses is recorded. Then, the process is repeated for the second mouse.
a.
Draw a tree diagram where the first stage represents the decision made by the first mouse, and
the second stage represents the decision made by the second mouse. Determine all four
possible decision outcomes for the two mice.
Name:_________________________________
M5L5
Accordino-Math 7
Date:_________
Period:________
Lesson 5: Using Tree Diagrams to
Represent a Sample Space and to Calculate
Probabilities
Exit Ticket
(3 points)
Draw a tree diagram representing the possible outcomes of flipping a coin and then rolling a six sided die.
Based on your outcomes, what is the probability of getting a heads and an even number?