Notes

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?
pic5-43. 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!”
Do you agree with Rachel? Why or why not?
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?
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.
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.

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.
While both players are making their choice at the same time, this game has two events in every turn. What are the two events?
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.
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.
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.
How many times would you expect Player A to win? Player B to win?
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.
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?
5-47. Identify the situations below as either dependent or independent events.
Flipping a “heads” on a quarter and then flipping another “heads.”
Choosing a jack from a standard deck of cards, not putting it back in the deck, and then choosing a king.
Picking a blue marble from a bag of marbles, putting it back, and then picking a blue marble again.
Rolling a 6 on a number cube three times in a row.
pic5-48. LEARNING LOG
In your Learning Log, make an entry that summarizes your understanding of independent and dependent events. Explain how to decide if two events are independent or dependent when looking at their likelihood. Give a few examples to support your thinking. Title your notes “Independent and Dependent Events” and include today’s date.
Text Box: MATH NOTES

Independent and Dependent Events

Two events are independent if the outcome of one event does not affect the outcome of the other event. For example, if you draw a card from a standard deck of playing cards but replace it before you draw again, the outcomes of the two draws are independent.
Two events are dependent if the outcome of one event affects the outcome of the other event. For example, if you draw a card from a standard deck of playing cards and do not replace it for the next draw, the outcomes of the two draws are dependent.
pic
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. Homework Help ✎
P(spinning a 3 on a spinner after having just spun a 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)
P(drawing a face card from a deck of cards after a jack was just drawn and replaced and the deck shuffled again)
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. Homework Help ✎
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?
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. Homework Help ✎
x = 9 cm
x = 0.5 cm Hint: Draw a diagram. Does your perimeter expression work?
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. Homework Help ✎
5-53. Copy and simplify the following expressions by combining like terms. Using algebra tiles may be helpful. Homework Help ✎
3 + 4x + 2 + 2x + 2x
8x + 4 − 3 − x
7x2 + 3x + 4 + 7x2 + 3x + 4
5x + 4 + x + x2 + 1