Determining a sample space and outcomes for an event: Exporiment... A bag has six balls labeled \( A, B, C, D, E \), and \( F \). One ball will be randomly picked, and its letter will be recorded as the outcome. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event of choosing the letter \( C \). If there is more than one element in the set, separate them with commas.

The sample space for this experiment, which includes all possible outcomes when picking one ball from the bag, is given by the set \( S = \{ A, B, C, D, E, F \} \). This means that any of the six labeled balls can be chosen, and each letter represents a potential outcome. The specific outcomes for the event of choosing the letter \( C \) is simply the set containing that one outcome, which is \( \{ C \} \). So, if you're lucky enough to pull out the ball labeled \( C \), that’s your winning moment!