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:

Step1: Determine all card - ball pairs

The box has cards numbered 1, 2, 3 and the bag has balls labeled A, B, C. For each card number (1, 2, 3), we can pair it with each ball label (A, B, C).

• When the card number is 1, the possible pairs are 1A, 1B, 1C.
• When the card number is 2, the possible pairs are 2A, 2B, 2C.
• When the card number is 3, the possible pairs are 3A, 3B, 3C.

Step2: Construct the sample space

Combining all these pairs, the sample space \( S=\{1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C\} \)

Step3: Find the event where the letter is B

We look for all pairs in the sample space where the letter is B. These are the pairs where the second part of the notation is B. So we have 1B, 2B, 3B.

Answer:

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