Pre-Calculus examples: Defining sample spaces for various experiments

📚 Quick Study Guide

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• Experiment: An activity with observable results.
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• Sample Space (S): The set of all possible outcomes of an experiment.
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• Event: A subset of the sample space.
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• Example 1: Tossing a coin: $S = \{Heads, Tails\}$
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• Example 2: Rolling a six-sided die: $S = \{1, 2, 3, 4, 5, 6\}$
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• Example 3: Drawing a card from a standard deck: $S = \{Ace of Hearts, 2 of Hearts, ..., King of Spades\}$
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• Tip: Always define the experiment clearly before determining the sample space.

Practice Quiz

1. What is the sample space for flipping a coin twice?
   1. {Heads, Tails}
   2. {Heads, Tails, Sides}
   3. {HH, HT, TH, TT}
   4. {H, T}
2. What is the sample space for rolling a four-sided die?
   1. {1, 2, 3, 4, 5, 6}
   2. {1, 3}
   3. {1, 2, 3, 4}
   4. {4}
3. What is the sample space for drawing a marble from a bag containing 1 red, 1 blue, and 1 green marble?
   1. {Red, Blue}
   2. {Red, Green}
   3. {Red, Blue, Green}
   4. {Marble}
4. What is the sample space for observing the color of a car?
   1. {Red, Blue, Green}
   2. {Color}
   3. {All possible colors}
   4. {Black, White, Silver}
5. What is the sample space for choosing a letter from the word 'SAMPLE'?
   1. {S, A, M, P, L, E}
   2. {A, E}
   3. {S, M, P}
   4. {SAMPLE}
6. What is the sample space for the number of heads when flipping 3 coins?
   1. {0, 1, 2}
   2. {0, 1, 2, 3}
   3. {1, 2, 3}
   4. {HHH, TTT}
7. What is the sample space for the seasons of the year?
   1. {Spring, Summer}
   2. {Winter, Autumn}
   3. {Hot, Cold}
   4. {Spring, Summer, Autumn, Winter}