Question

Joe flips this coin once and picks one card from a deck. The deck has these cards.
1 2 3 4 5 6
Which table represents the sample space of this compound event?

Answer 1

To represent the sample space of the compound event where Joe flips a coin and picks one card from a deck with cards numbered 1 to 6, we need to consider the outcomes of both events.

1. **Coin Flip Outcomes**: There are 2 possible outcomes for the coin flip: Heads (H) or Tails (T).
2. **Card Draw Outcomes**: There are 6 possible outcomes for picking a card: 1, 2, 3, 4, 5, and 6.

To form the sample space, we combine the outcomes from the coin flip with the outcomes from the card draw. This can be represented in a table or a list.

### Sample Space Representation

The sample space can be written as pairs (Coin Outcome, Card Outcome):

1. (H, 1)
2. (H, 2)
3. (H, 3)
4. (H, 4)
5. (H, 5)
6. (H, 6)
7. (T, 1)
8. (T, 2)
9. (T, 3)
10. (T, 4)
11. (T, 5)
12. (T, 6)

### Sample Space Table:

| Coin Outcome | Card Outcome | Combined Outcome |
|--------------|--------------|------------------|
| H | 1 | (H, 1) |
| H | 2 | (H, 2) |
| H | 3 | (H, 3) |
| H | 4 | (H, 4) |
| H | 5 | (H, 5) |
| H | 6 | (H, 6) |
| T | 1 | (T, 1) |
| T | 2 | (T, 2) |
| T | 3 | (T, 3) |
| T | 4 | (T, 4) |
| T | 5 | (T, 5) |
| T | 6 | (T, 6) |

Thus, the sample space of this compound event consists of the 12 combined outcomes listed above.