Questions: If a person draws a playing card and checks its suit and then spins a three-space spinner, describe the sample space of possible outcomes using C, D, H, S for the card outcomes and 1, 2, 3 for the spinner outcomes. Type the outcomes in the form C 1 or 1 C , which would be the outcome of drawing a club and spinning a 1.

If a person draws a playing card and checks its suit and then spins a three-space spinner, describe the sample space of possible outcomes using C, D, H, S for the card outcomes and 1, 2, 3 for the spinner outcomes. Type the outcomes in the form C 1 or 1 C , which would be the outcome of drawing a club and spinning a 1.
Transcript text: If a person draws a playing card and checks its suit and then spins a three-space spinner, describe the sample space of possible outcomes using C, D, H, S for the card outcomes and 1, 2, 3 for the spinner outcomes. Type the outcomes in the form C 1 or 1 C , which would be the outcome of drawing a club and spinning a 1. The sample space is $S=\{$
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Solution

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Solution Steps

To solve this problem, we need to determine the sample space of a combined event involving drawing a card and spinning a spinner. The card can be one of four suits: Clubs (C), Diamonds (D), Hearts (H), or Spades (S). The spinner can land on one of three numbers: 1, 2, or 3. The sample space is the set of all possible outcomes, which is the Cartesian product of the two sets: the set of card suits and the set of spinner outcomes.

Step 1: Define the Sets of Outcomes

To determine the sample space, we first define the sets of possible outcomes for each event. The card can be one of four suits: Clubs (C), Diamonds (D), Hearts (H), or Spades (S). The spinner can land on one of three numbers: 1, 2, or 3.

Step 2: Calculate the Cartesian Product

The sample space is the Cartesian product of the two sets: the set of card suits and the set of spinner outcomes. This means we pair each card suit with each spinner outcome.

Step 3: List the Sample Space

The sample space \( S \) is the set of all possible outcomes, which can be listed as follows: \[ S = \{ \text{C 1}, \text{C 2}, \text{C 3}, \text{D 1}, \text{D 2}, \text{D 3}, \text{H 1}, \text{H 2}, \text{H 3}, \text{S 1}, \text{S 2}, \text{S 3} \} \]

Final Answer

The sample space is: \[ \boxed{S = \{ \text{C 1}, \text{C 2}, \text{C 3}, \text{D 1}, \text{D 2}, \text{D 3}, \text{H 1}, \text{H 2}, \text{H 3}, \text{S 1}, \text{S 2}, \text{S 3} \}} \]

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