Question

a box has three cards numbered 1, 2, and 3.
a bag has three balls labeled a, b, and c
henry 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 b.

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.

sample space:

event that the letter chosen is b :

Explanation:

Sample Space

Step1: List card - ball combinations

For card 1, we can pair it with each ball (A, B, C), getting 1A, 1B, 1C.
For card 2, we pair it with each ball, getting 2A, 2B, 2C.
For card 3, we pair it with each ball, getting 3A, 3B, 3C.

Step2: Combine all combinations

The sample space is the set of all these combinations.

Step1: Identify combinations with letter B

We look for all outcomes where the letter is B. So we take each card number (1, 2, 3) and pair it with B.

Step2: List the combinations

The combinations are 1B, 2B, 3B.

Answer:

Sample space: {1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C}

Event that the letter chosen is B