Analyzing Combined Sample Space of Coin Toss and Die Roll
The image shows a question that reads:
"A fair coin is tossed and a fair die is thrown right down the ramp. The sample space consists of a coin"
b) Union of the two
c) Write "Combinations" of this experiment
To solve this question we need to describe the combined sample space for both a coin toss and a die roll, and then write down all the possible combinations (outcomes).
A fair coin has two possible outcomes: Heads (H) and Tails (T).
A fair six-sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6.
The sample space for both a coin toss and die roll consists of each coin outcome paired with each die outcome. Therefore:
- For a coin landing on Heads, the die can land on any of the six sides, which makes the sample space: (H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6);
- For a coin landing on Tails, the die can also land on any of the six sides, which makes the sample space: (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6).
The union of the two would be the entire sample space as there are no overlapping elements between a coin toss and a die roll.
Combine all these possibilities together to get the full "Combinations" of this experiment:
(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6),
(T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6).
These represent all the possible outcomes when a coin is tossed and a die is thrown at the same time. There are a total of 2 (coin outcomes) x 6 (die outcomes) = 12 possible outcomes in the sample space.
