List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card from a set of 6 cards numbered 1 through 6.
S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}
Explanation
The textbook defines a sample space as the list of all possible outcomes of an experiment. For the simultaneous tossing of a coin and drawing of a card, we must find the combinations of both individual sample spaces. A coin has 2 outcomes (Heads, Tails), and a card numbered 1 through 6 has 6 outcomes. Combining these gives a total sample size of = 12 possible outcomes, which are listed as ordered pairs.
Solution Steps
Step 1: Identify the sample space for tossing a coin, which is {H, T}.
Step 2: Identify the sample space for drawing a card numbered 1 through 6, which is {1, 2, 3, 4, 5, 6}.
Step 3: Combine each coin outcome with each card outcome to list all 12 elements of the simultaneous experiment: S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}.