Consider the experiment of tossing a fair two-sided coin, noting the side landing up, and then spinning a spinner with 3 equal regions (red, blue, green), noting the color. State t... Consider the experiment of tossing a fair two-sided coin, noting the side landing up, and then spinning a spinner with 3 equal regions (red, blue, green), noting the color. State the sample space for this experiment. Assume heads = H, tails = T, red = R, blue = B, and green = G.
Understand the Problem
The question asks to determine the sample space for an experiment involving tossing a fair two-sided coin and spinning a spinner with three equal regions (red, blue, green). The student needs to identify all possible outcomes.
Answer
$S = \{(H, R), (H, B), (H, G), (T, R), (T, B), (T, G)\}$
Answer for screen readers
$S = {(H, R), (H, B), (H, G), (T, R), (T, B), (T, G)}$
Steps to Solve
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List the possible outcomes of tossing the coin The coin can land either heads (H) or tails (T).
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List the possible outcomes of spinning the spinner The spinner can land on red (R), blue (B), or green (G).
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Combine the outcomes of both events to form the sample space We need to list all possible pairs of outcomes, where the first element of the pair is the result of the coin toss and the second element is the result of the spinner. The sample space S is then: $S = {(H, R), (H, B), (H, G), (T, R), (T, B), (T, G)}$
$S = {(H, R), (H, B), (H, G), (T, R), (T, B), (T, G)}$
More Information
The sample space represents all possible outcomes of the combined experiment. There are 2 possible outcomes for the coin and 3 for the spinner, leading to $2 \times 3 = 6$ total outcomes in the sample space.
Tips
A common mistake is to list the elements of the events separately, like ${H, T, R, B, G}$, which doesn't correctly represent the combined outcomes. Another mistake would be to forget one or more of the possible combinations.
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