Final answer:
The sample space of the experiment where A, B, and C take turns flipping a coin until someone gets a head can be defined as S = {1, 01, 001, 0001, ...}. The outcomes represent the number of tosses it takes for one of the players to get a head, with 0 representing tails. The sample space shows all possible outcomes of the experiment.
Step-by-step explanation:
The sample space S you've defined represents all possible outcomes of the coin-flipping game. Each element in the sample space represents a sequence of coin flips, where 0 represents tails and 1 represents heads. The sequence starts with one flip and can continue indefinitely with additional flips.
Let's break down a few elements in the sample space to illustrate:
1 : This represents the outcome where the first person flips the coin and gets heads on the first attempt. The game ends, and the first person wins.
01 : This represents the outcome where the first person flips tails, and then the second person flips heads on their first attempt. The game ends, and the second person wins.
001 : This represents the outcome where the first person flips tails, the second person flips tails, and then the third person flips heads on their first attempt. The game ends, and the third person wins.
And so on. The pattern continues, with each element in the sample space representing a possible sequence of coin flips where the first appearance of a head determines the winner of the game. The ellipsis (...) indicates that the sequence can continue with additional flips.
It's worth noting that the sample space includes infinite sequences because the game could theoretically go on indefinitely if all flips result in tails. However, the game is guaranteed to end once a head appears.