Question

a box has three cards numbered 1, 2, and 3. a bag has three balls labeled a, b, and c. bob will randomly pick a card from the box and record the number chosen. then he will randomly pick a ball from the bag and record the letter chosen. give the sample space describing all possible outcomes. then give all of the outcomes for the event that the letter chosen is c. use the format 1a to mean that the number chosen is 1 and the letter chosen is a. if there is more than one element in the set, separate them with commas.

Explanation:

Step1: Determine sample space

For each card number (1, 2, 3), there are 3 ball - letter combinations.
$$\{1A,1B,1C,2A,2B,2C,3A,3B,3C\}$$

Step2: Find event with letter C

Select elements from sample space where letter is C.
$$\{1C,2C,3C\}$$

Answer:

Sample space: $\{1A,1B,1C,2A,2B,2C,3A,3B,3C\}$
Event that the letter chosen is $C$: $\{1C,2C,3C\}$