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WDYE? 2.3: Designing a Fair Game
Learning Target: I will analyze the fairness of a game by
listing all possible outcomes in a tree diagram and
determining theoretical probabilities.
HW: 1) Get a parent signature on WDYE packet #1
2)Complete the WDYE Investigation 2-3 p. 4 and
Correct with the Zaption video: WDYE 2.3
1. Warm Up: Show ALL work with Proper notation!!
A bag contains marbles: 3 red, 7 blue, and 6 yellow.
• What is the probability of drawing a marble
that is not red?
• What is the probability of drawing a marble that is
either red or blue?
Warm-Up Question
Show ALL work with Proper notation!!
• A bag contains 3 red marbles, 7 blue marbles, & 6 yellow
marbles.
– What is the probability of drawing
a marble that is not red? P(not red) = 1 – P(red)
= 1 - 3/16
= 13/16
– What is the probability of drawing a marble that is
either red or blue?
P(R or B) = P(Red) + P (Blue)
= 3/16 + 7/16
= 10/16
= 5/8
Inv. 2-3 packet
p. 2
Tossing Three Coins
Events:
Start
tree diagramis an illustration using branches to show
A _____diagram
the sample space of an event.
The ________
space is another name for the set of possible
sample space
outcomes of an event.
Events:
Start
1. The sample space for tossing three coins
is the list of all possible outcomes.
{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
2. There are 8 possible outcomes, and they
are all equally likely.
P (3 coins match) = 2/8 or 1/4
P (exactly 2 coins match) = 6/8 or 3/4
No, this is not a fair game. Tevy has more
chances to score a point (2 coins match),
so he is more likely to win.
(Hint: Write a proportion.)
You would expect
exactly 2 coins to match ¾ of the time.
¾ of 24 = 18
P (exactly 2 coins match) = 18/24 trials
X3
Santo means that all 3 coins match
sometimes. Tevy is saying the
probability is less than ½.
If time, model building another tree diagram.
Virtual nerd video example slides 10-13.
Challenge slides (no answers) slides 14-15
(Blue, Purple, Red)
(Jeans, Skirt)
(Sandals, High Heels)
X
1. What is the probability of not wearing a red shirt?
P(not R) =
P(P + B) = 1/3 +1/3
= 2/3
OR
P(not R) = 1- P(R)
= 1 – 1/3
= 2/3
(Blue, Purple, Red)
(Jeans, Skirt)
(Sandals, High Heels)
What is the probability of wearing an outfit
with jeans and sandals?
P(J and S) = 3/12 = 1/4
(Blue, Purple, Red)
(Jeans, Skirt)
(Sandals, High Heels)
What is the probability of wearing
either a purple or blue shirt?
P(P and B) = 1/3 + 1/3 = 2/3
Challenge: Karen and Mia invent another game. They roll
a number cube twice and read the digits shown as a twodigit number. So, if Karen gets a 6 and a 2, she has 62.
Create a tree diagram for this situation. List all of the
possible outcomes.
Events:
Start
b. What are all of the possible outcomes when you roll a number
cube twice and create a two-digit number?
c. What is the least number possible?
d. What is the greatest number possible?
e. Are all numbers equally likely?
f. Suppose Karen wins on any prime number and Mia wins on any
multiple of 4. Explain how to decide who is more likely to win.
WDYE? 2.3: Designing a Fair Game
Did I reach my Learning Target?
I will analyze the fairness of a game by listing
all possible outcomes in a tree diagram and
determining theoretical probabilities.
HW: Complete the WDYE Investigation 2-3 p. 4 and
Correct with the Zaption video: WDYE 2.3