7.SP.8b: Represent sample spaces for compound events using methods...

Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.



Joe has a bag containing 8 red sweets, 9 yellow ones and 11 green. He takes out a sweet and eats it, then, he takes out a second sweet. What is the probability that both the sweets are red?
Joe has a bag containing 8 red sweets, 9 yellow ones and 11 green. He takes out a sweet and eats it, then, he takes out a second sweet. What is the probability that both the sweets are red?


Karl is thinking of holding a mini-lottery to raise money.
Karl will sell tickets like this for $1 each.

Each player must put a cross through 2 numbers on the ticket and hand it in. At the end of the week Karl will draw out two balls from a bag.

Every player who has chosen the same two numbers as shown on the balls will win a cash prize of $10.
(a) How many ways are there of choosing two different numbers on the ticket? Show all your work.
(b) Will the lottery be a good money raiser? Describe your reasoning.
Karl is thinking of holding a mini-lottery to raise money.
Karl will sell tickets like this for $1 each.

Each player must put a cross through 2 numbers on the ticket and hand it in. At the end of the week Karl will draw out two balls from a bag.

Every player who has chosen the same two numbers as shown on the balls will win a cash prize of $10.
(a) How many ways are there of choosing two different numbers on the ticket? Show all your work.
(b) Will the lottery be a good money raiser? Describe your reasoning.


Lindsay Lohan is playing with a die. Lindsay Lohan cups her hand, hopes for a six, and rolls a six. Lindsay Lohan is convinced that she is lucky. Frank Ocean comes along, drops another die on the table and tells Lindsay Lohan to do it again with both of them. "I can do it as easily with two as with one," says Lindsay Lohan.

(a) What is the probability of rolling a six?
(b) What is the probability of rolling double sixes?
Lindsay Lohan is playing with a die. Lindsay Lohan cups her hand, hopes for a six, and rolls a six. Lindsay Lohan is convinced that she is lucky. Frank Ocean comes along, drops another die on the table and tells Lindsay Lohan to do it again with both of them. "I can do it as easily with two as with one," says Lindsay Lohan.

(a) What is the probability of rolling a six?
(b) What is the probability of rolling double sixes?
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Miley Cyrus is playing a game with dice. The object of the game is to roll the same number on both dice. Taylor Swift decides she is going to mess with Miley Cyrus by rigging it so that i will never land on two. How does this change Miley Cyrus's probability of success?
Miley Cyrus is playing a game with dice. The object of the game is to roll the same number on both dice. Taylor Swift decides she is going to mess with Miley Cyrus by rigging it so that i will never land on two. How does this change Miley Cyrus's probability of success?
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Sally has made a Spinner Bingo game for her class.

"Write down 9 different numbers on your card. I will spin both spinners and add up the two numbers I get. If you have that total on your Bingo card, you cross it off. The first person to cross off all the numbers wins the prize," says Sally.
(a) Here are three Bingo cards the players made

Which card has the best possible chance of winning? Give reasons for your answer.
(b) On the worksheet, fill in a card so that it has the best chance of winning.

(c) Explain how you chose the numbers for your card.
Sally has made a Spinner Bingo game for her class.

"Write down 9 different numbers on your card. I will spin both spinners and add up the two numbers I get. If you have that total on your Bingo card, you cross it off. The first person to cross off all the numbers wins the prize," says Sally.
(a) Here are three Bingo cards the players made

Which card has the best possible chance of winning? Give reasons for your answer.
(b) On the worksheet, fill in a card so that it has the best chance of winning.

(c) Explain how you chose the numbers for your card.


Ann is in charge of a Lucky Dip to raise money for charities.

Each barrel contains an equal number of red, green, white and black balls.
The balls are buried in sawdust so that you cannot see them before you pick one out
To play the game, you give Ann your 25¢, then you pick one ball from each barrel.
You win $5 if all three balls are the same color.

(a) Calculate the probability that you will win the $5 if you play once.
(b) Do you think that the Lucky Dip will raise money for the local charities? Show your calculations
(c) Ann wants to change the game so as to increase the amount of money it makes for the charities.
Describe two different kinds of change that she could make to the Lucky Dip and find how much is likely to be raised for the charities after each change. Show all your calculations.
Ann is in charge of a Lucky Dip to raise money for charities.

Each barrel contains an equal number of red, green, white and black balls.
The balls are buried in sawdust so that you cannot see them before you pick one out
To play the game, you give Ann your 25¢, then you pick one ball from each barrel.
You win $5 if all three balls are the same color.

(a) Calculate the probability that you will win the $5 if you play once.
(b) Do you think that the Lucky Dip will raise money for the local charities? Show your calculations
(c) Ann wants to change the game so as to increase the amount of money it makes for the charities.
Describe two different kinds of change that she could make to the Lucky Dip and find how much is likely to be raised for the charities after each change. Show all your calculations.


Taylor Swift and three friends have a tradition of meeting every week for lunch. Each week they use a spinner to determine who gets to choose the next place.



Taylor Swift has gotten to choose three times in a row.
(a) What's the probability of such an occurrence?
(b) What's the probability that Taylor Swift gets to choose the fourth week as well?
Taylor Swift and three friends have a tradition of meeting every week for lunch. Each week they use a spinner to determine who gets to choose the next place.



Taylor Swift has gotten to choose three times in a row.
(a) What's the probability of such an occurrence?
(b) What's the probability that Taylor Swift gets to choose the fourth week as well?
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Taylor Swift and Kendrick Lamar are playing a simple game of chance. They take turns spinning a quarter on the table. If it lands heads, Taylor Swift wins. If it lands tails, Kendrick Lamar wins. The first four rolls are all heads. "That's impossible!" yells Kendrick Lamar, "It must be a loaded coin!" "Actually, it's unlikely, but not impossible," responds Taylor Swift.

(a) What is the probability of this event?
(b) What is the probability of the next flip landing tails?
(c)How many tails in a row is truly impossible?
Taylor Swift and Kendrick Lamar are playing a simple game of chance. They take turns spinning a quarter on the table. If it lands heads, Taylor Swift wins. If it lands tails, Kendrick Lamar wins. The first four rolls are all heads. "That's impossible!" yells Kendrick Lamar, "It must be a loaded coin!" "Actually, it's unlikely, but not impossible," responds Taylor Swift.

(a) What is the probability of this event?
(b) What is the probability of the next flip landing tails?
(c)How many tails in a row is truly impossible?
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Ella is teaching her little brother Sammy to play a memory game.
She starts with 4 cards, 2 have a picture of an apple on them and 2 have a picture of bananas.


The cards are laid on the table with the pictures hidden, and then mixed up. Ella says ‘you can turn over 2 cards and you win if they are the same’.
(a) Sammy turns over 1 card (an apple), and another card. What is the probability that the second card has an apple on it? Explain how you figured it out.

(b) Sammy did not get 2 cards the same so Ella turns the cards back over so that the pictures do not show, but she does not mix up the cards.

Sammy is good at remembering where things are. He turns over 1 card and then another. How should he choose the first card to turn over so that he can be sure to win?
(c) Ella adds 2 cards with pictures of an orange, making 6 cards all together.

She lays all the cards down with the pictures hidden and mixes them up.

Sammy turns over 1 card and then another. What is the probability that they are both the same? Explain how you figured it out.
(d) What is the probability that they both have pictures of a banana? Show how you worked it out.
Ella is teaching her little brother Sammy to play a memory game.
She starts with 4 cards, 2 have a picture of an apple on them and 2 have a picture of bananas.


The cards are laid on the table with the pictures hidden, and then mixed up. Ella says ‘you can turn over 2 cards and you win if they are the same’.
(a) Sammy turns over 1 card (an apple), and another card. What is the probability that the second card has an apple on it? Explain how you figured it out.

(b) Sammy did not get 2 cards the same so Ella turns the cards back over so that the pictures do not show, but she does not mix up the cards.

Sammy is good at remembering where things are. He turns over 1 card and then another. How should he choose the first card to turn over so that he can be sure to win?
(c) Ella adds 2 cards with pictures of an orange, making 6 cards all together.

She lays all the cards down with the pictures hidden and mixes them up.

Sammy turns over 1 card and then another. What is the probability that they are both the same? Explain how you figured it out.
(d) What is the probability that they both have pictures of a banana? Show how you worked it out.


Selena Gomez and Emma Watson are playing a board game. Selena Gomez is playing the black piece, and it is her turn. Selena Gomez rolls two dice to determine how far to move.



(a) What is the probability that Selena Gomez passes Emma Watson on this move?
(b) What is the probability that Selena Gomez wins on this move?
(c) What is the probability that Emma Watson wins on the next move?
Selena Gomez and Emma Watson are playing a board game. Selena Gomez is playing the black piece, and it is her turn. Selena Gomez rolls two dice to determine how far to move.



(a) What is the probability that Selena Gomez passes Emma Watson on this move?
(b) What is the probability that Selena Gomez wins on this move?
(c) What is the probability that Emma Watson wins on the next move?
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Represent sample spaces for compound events



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