Sample Space

The sample space includes all possible outcomes of Dan randomly picking a card from the box and a ball from the bag. Each outcome can be represented in the format $nX$, where $n$ is the number chosen from the box and $X$ is the letter chosen from the bag.

The possible outcomes are:

$\text{Sample Space} = \{ 1A, 1B, 1C, 2A, 2B, 2C, 3A, 3B, 3C \}$

Event: The letter chosen is B

The event where the letter chosen is $B$ includes all outcomes where the second element of the pair is $B$.

The possible outcomes for this event are:

$\text{Event} = \{ 1B, 2B, 3B \}$

Would you like more details or have any questions about the solution?

Here are 8 related questions for further practice:

1. What is the probability of selecting a 2 and a B?
2. If Dan adds another ball labeled D, what will be the new sample space?
3. How many outcomes are there if Dan first picks a ball and then a card?
4. What is the probability of selecting an A from the bag?
5. How does the sample space change if two cards are selected without replacement?
6. What is the probability that the number chosen is 1 or the letter chosen is C?
7. If the cards are labeled 1, 2, and 3, and the balls are labeled X, Y, and Z, what is the new sample space?
8. How does the event set change if the letter chosen is A instead of B?

Tip: Understanding the concept of sample space is fundamental in probability theory. It lays the groundwork for calculating probabilities of different events.