Question

olivia is choosing a pair of socks and a pair of shoes. for the socks, she can choose from red and blue and for the shoes, she can choose from sandals, loafers, sneakers, and boots. what is the sample space of one pair of socks and one pair of shoes? complete the table below to find all of the possible outcomes of this experiment. sandals loafers sneakers boots red blue red blue sandals loafers sneakers boots

Explanation:

Step1: Analyze Sock and Shoe Combinations

For each sock color (Red, Blue), pair with each shoe type (Sandals, Loafers, Sneakers, Boots).

• Red Socks:
• With Sandals: (Red, Sandals)
• With Loafers: (Red, Loafers)
• With Sneakers: (Red, Sneakers)
• With Boots: (Red, Boots)
• Blue Socks:
• With Sandals: (Blue, Sandals)
• With Loafers: (Blue, Loafers)
• With Sneakers: (Blue, Sneakers)
• With Boots: (Blue, Boots)

Step2: Fill the Table

In the table, for each cell (row: sock color, column: shoe type), write the pair.

• Red row, Sandals column: Red, Sandals
• Red row, Loafers column: Red, Loafers
• Red row, Sneakers column: Red, Sneakers
• Red row, Boots column: Red, Boots
• Blue row, Sandals column: Blue, Sandals
• Blue row, Loafers column: Blue, Loafers
• Blue row, Sneakers column: Blue, Sneakers
• Blue row, Boots column: Blue, Boots

Answer:

The sample space (all possible outcomes) is: {(Red, Sandals), (Red, Loafers), (Red, Sneakers), (Red, Boots), (Blue, Sandals), (Blue, Loafers), (Blue, Sneakers), (Blue, Boots)}.
Filling the table:

• Red - Sandals: Red, Sandals
• Red - Loafers: Red, Loafers
• Red - Sneakers: Red, Sneakers
• Red - Boots: Red, Boots
• Blue - Sandals: Blue, Sandals
• Blue - Loafers: Blue, Loafers
• Blue - Sneakers: Blue, Sneakers
• Blue - Boots: Blue, Boots