7th 7-5 Determine Outcomes of Compound Events

A soccer tournament assigns a unique​ two-color uniform to each team using the colors yellow (Y)​, green (G)​, orange (O)​, and purple (P). Each uniform is mostly one color with a different colored stripe. Write an organized list using the format​ (main color, stripe​ color) to represent the sample space.

• (Y​,G​), (Y​,O​), (Y​,P​), (G​,Y​), (G​,O​), (G​,P​), (O​,Y​), ​(O​,G​), (O​,P​), (P​,Y​), ​(P​,G​), (P​,O​)

• (Y​,G​), ​(Y​,O​), (Y​,P​), (G​,O​), (G​,P​), (O​,P​)

• (Y​,G​,O​,P​), (G​,O​,P​,Y​), ​(O​,P​,Y​,G​), ​(P​,Y​,G​,O​)

• (Y​,G​), (Y​,O​), (Y​,P​), (G​,Y​), (G​,G​), (G​,O​), (G​,P​), ​(O​,Y​), ​(O​,G​), ​(O​,O​), (O​,P​), (P​,Y​), (P​,G​), ​(P​,O​)

A soccer tournament assigns a unique​ two-color uniform to each team using the colors yellow (Y)​, green (G)​, orange (O)​, and purple (P). Each uniform is mostly one color with a different colored stripe. Write an organized list using the format​ (main color, stripe​ color) to represent the sample space. Does it matter what order you list the different ways to assign the uniform​ colors? Explain your reasoning.

• Yes (Y,O) means yellow main color, and orange stripe

• Yes (Y,O) means yellow stripe and Orange main color

• No (Y,O) means yellow main color, and orange stripe

• No (Y,O) means yellow stripe and Orange main color

A designer has designed two pairs of pants (P1 and P2) and five tops (T1, T2, T3, T4, and T5) to create outfits. Use a tree diagram to display the sample space of possible outfits if she chooses pants and then a top for each outfit.

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A designer has designed two pairs of pants (P1 and P2) and five tops (T1, T2, T3, T4, and T5) to create outfits. Use a tree diagram to display the sample space of possible outfits if she chooses pants and then a top for each outfit. How many different outfits could she ​create?

• 10

• 6

• 8

• 12

Two friends each choose a slice of pizza with one topping. The toppings to choose from are tomatoes (T), jalapeños ​(J), onions (O), and eggplant (E). Write an organized list using the format (Friend 1, Friend 2) to represent the sample space of topping combinations.

• (T​,J​), (T​,O​), ​(T​,E​), (J​,O​), ​(J​,E​), ​(O​,E​)

• ​(T​,T​), (T​,J​), ​(T​,O​), (T​,E​)

  (J​,T​), ​(J​,J​), (J​,O​), (J​,E​)

  ​(O​,T​), (O​,J​), ​(O​,O​), ​(O​,E​)

  ​(E​,T​), ​(E​,J​), ​(E​,O​), ​(E​,E​)

• (T​,T​)

  ​(J​,J​)

  ​(O​,O​)

  ​(E​,E​)

• (T​,J​), ​(T​,O​), ​(T​,E​)

  ​(J​,T​), ​(J​,O​), ​(J​,E​)

  ​(O​,T​), ​(O​,J​), ​(O​,E​)

  ​(E​,T​), ​(E​,J​), (E​,O​)

Use a table to show the sample space of​ two-digit numbers using the digits 1,4,5,9.

Use the column label as the tens digit and the row label as the ones digit to complete the table that represents the sample space of​ two-digit numbers.

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A museum gift shop sells hats with embroidered logos of the museum. The hats are available in​ small, medium, and large sizes. They are available in the colors red and green. Make a tree diagram to represent all possible varieties of hats sold at the museum.

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Vincent forgot the last two digits for his bicycle lock. He remembers that each digit is 5 through 9. Use a table to show all possible pairs of digits.

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A table with 3 rows and 5 columns can represent the sample space of combinations of a number between 1 and 3 followed by a letter between A and E in the English alphabet.

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You roll a fair number cube, then roll it again. How many possible outcomes are there?