Lesson 5.2.3
HW: 5-49 to 5-53
Learning Target: Scholars will find probabilities of compound independent events and will determine
whether pairs of events are dependent or independent.
When you studied probability in earlier lessons, you focused on probabilities of single events (for
example, one draw of a card, or picking one cube from a bag). You also examined probabilities of either
one or another of two events occurring (for example, winning either a raffle ticket or cash; drawing either
a king or queen). In this lesson, you will begin to investigate when one and another event both occur,
such as flipping two coins or spinning a spinner multiple times. Throughout this lesson, use these
questions to help focus your team’s discussion:
 Does the result of one event affect the other?
 How many possibilities are there?
5-43. In Chapter 1, you met Chris and her older sister, Rachel, who made a system for determining which
one of them washes the dishes each night. Chris has been washing the dishes much more than she feels is
her fair share, so she has come up with a new system. She has proposed to Rachel that they get two coins,
and each day she and Rachel will take a coin and flip their coins at the same time. If the coins match,
Chris washes the dishes; if they do not match, Rachel washes the dishes. Explore using CPM Probability
eTool (CPM).
 Rachel thinks that this is a good idea and that her little sister is very silly! She thinks to herself, “Since
there are two ways to match the coins, Heads-and-Heads or Tails-and-Tails, and only one non-match,
Heads-and-Tails, then Chris will STILL wash the dishes more often. Ha!”
1. Do you agree with Rachel? Why or why not?
2. Does it matter if they flip the coins at the same time? That is, does the result of one coin flip
depend on the other coin flip?
3. What are all of the possible outcomes when the girls flip their coins? Organize the
possibilities. Use the word “and” when you are talking about both one thing and another
occurring.
4. Look at your list from part (c). Imagine that the coins are a penny and a nickel instead of two of
the same coin. Does your list include both the possibilities of getting a heads on the penny and
tails on the nickel and vice versa? If not, be sure to add them to your list.
5. Is Rachel right? Does this method give her an advantage, or is this a fair game? What is the
theoretical probability for each girl’s washing the dishes?
5-44. ROCK-PAPER-SCISSORS
Read the rules for the Rock-Paper-Scissors game below. Is this a fair game? Discuss this question with
your team.
How to Play
At the same time as your partner, shake your fist three times and then display either a closed fist for
"rock," a flat hand for "paper," or a partly closed fist with two extended fingers for "scissors." Rock beats
scissors (because rock blunts scissors), scissors beats paper (because scissors cut paper), and paper beats
rock (because paper can wrap up a rock). If you both show the same symbol, repeat the round.
1. While both players are making their choice at the same time, this game has two events in every
turn. What are the two events?
2. If you and a partner are playing this game and you both “go” at the same time, does your choice
affect your partner’s choice? Explain.
3. Are the two events in this game dependent (where the outcome of one event affects the outcome
of the other event) or independent (where the outcome of one event does not affect the outcome
of the other event)? Explain your reasoning.
4. Work with your team to determine all of the possible outcomes of a game of rock-paper-scissors,
played by two people (call them Person A and Person B). Be sure to include the word “and.” For
each outcome, indicate which player wins or if there is a tie. Be prepared to share your strategies
for finding the outcomes with the class.
5-45. Is Rock-Paper-Scissors a fair game? How can you tell?
5-46. Imagine that two people, Player A and Player B, were to play rock-paper-scissors 12 times.
1. How many times would you expect Player A to win? Player B to win?
2. Now play rock-paper-scissors 12 times with a partner. Record how many times each player wins
and how many times the game results in a tie.
3. How does the experimental probability for the 12 games that you played compare to the
theoretical probability that each of you will win? Do you expect them to be the same or
different? Why?
5-49. For each of the following probabilities, write “dependent” if the outcome of the second event
depends on the outcome of the first event and “independent” if it does not.
1. P(spinning a 3 on a spinner after having just spun a 2)
2. P(drawing a red 6 from a deck of cards after the 3 of spades was just drawn and not
returned to the deck)
3. P(drawing a face card from a deck of cards after a jack was just drawn and replaced and
the deck shuffled again)
4. P(selecting a lemon-lime soda if the person before you reaches into a cooler full of
lemon-lime sodas, removes one, and drinks it)
5-50. Skye’s Ice Cream Shoppe is Mario’s favorite place to get ice cream. Unfortunately, because he was
late arriving there, his friends had already ordered. He did not know what they ordered for him. They
told him that it was either a waffle cone or a sundae and that the ice cream flavor was apricot, chocolate,
or blackberry.
5.
6.
7.
8.
Make a list of all of the possible ice cream orders.
What is the probability that Mario will get something with apricot ice cream?
What is the probability that he will get a sundae?
What is the probability that he will get either something with chocolate or a waffle cone
with blackberry?
9. What is the probability that he will get orange sherbet?
5-51. On your paper, sketch the algebra tile shape shown at right. Write
expressions for the area and perimeter of the shape. Then calculate the area and perimeter of the
shape for each x-value.
10. x = 9 cm
11. x = 0.5 cm
12. x = 15 cm
5-52. Elin has made twenty-nine note cards for her friends. She plans to send out a total of
forty cards. What percentage of the cards has she finished? Represent your work clearly on your paper.
5-53. Copy and simplify the following expressions by combining like terms. Using algebra tiles may be
helpful.
13.
14.
15.
16.
3 + 4x + 2 + 2x + 2x
8x + 4 − 3 − x
7x2 + 3x + 4 + 7x2 + 3x + 4
5x + 4 + x + x2 + 1
Lesson 5.2.3

5-43. See below:
1. Answers vary, some students might agree with Rachel and others might begin to
think about how the coins could be Heads-Tails or Tails-Heads.
2. No
3. There are four possibilities: H and H, H and T, T and H, and T and T
4. Students check list from part (c).
5. No, this method is fair, each girl has a probability of

for washing the dishes.
5-44. See below:
1. Player 1’s choice or play and Player 2’s choice or play.
2. No, each person doesn't know what the other is going to do.
3. Independent, the choices by each partner do not affect each other.
4. With Player A’s choice first, then Player B’s: R-and-R (tie), R-and-P (B wins), Rand-S (A wins), P-and-R (A wins), P-and-P (tie), P-and-S (B wins), S-and-R (B
wins), S-and-P (A wins), S-and-S (tie)

5-45. Yes, there is a
or there is a tie.

5-46. See below:
1. 4 times. 4 times
2. Answers vary.
3. Answers vary. It is likely that the experimental results will not be exactly the
same as the theoretical prediction.

5-49. See below:
1. independent
2. dependent
3. independent
4. independent

5-50. See below:
1. WA, WC, WB, SA, SB, SC
probability for each outcome: Person A wins, Person B wins,
2.
3.
4.
5. 0
+
=

5-51. A = 3x + 3, P = 2x + 10
1. P = 28 cm, A = 30 sq cm
2. P = 11 cm, A = 4.5 sq cm
3. P = 40 cm, A = 48 sq cm

5-52. 72.5%; Possible reasoning:

5-53.
1.
2.
3.
4.
See below:
8x + 5
7x + 1
14x2 + 6x + 8
x2 + 6x + 5