Question

An experiment consists of spinning a spinner that has 4 areas numbered 1 to 4 followed by flipping a coin. How many outcomes are in the sample space, and which outcomes would be in the event “a number greater than 2”?(1 point)
Responses

There are 8 outcomes in the sample space. The event “a number greater than 2” includes {3H, 4H}
.
There are 8 outcomes in the sample space. The event “a number greater than 2” includes left brace 3 upper H comma 4 upper H right brace .

There are 8 outcomes in the sample space. The event “a number greater than 2” includes {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T}
.
There are 8 outcomes in the sample space. The event “a number greater than 2” includes left brace 1 upper H comma 1 upper T comma 2 upper H comma 2 upper T comma 3 upper H comma 3 upper T comma 4 upper H comma 4 upper T comma right brace .

There are 8 outcomes in the sample space. The event “a number greater than 2” includes {3H, 3T, 4H, 4T}
.
There are 8 outcomes in the sample space. The event “a number greater than 2” includes left brace 3 upper H comma 3 upper T comma 4 upper H comma 4 upper T right brace .

There are 4 outcomes in the sample space. The event “a number greater than 2” includes {3H, 3T, 4H, 4T}
.

Answer 1

To determine the total number of outcomes in the sample space, we need to consider the spinner and the coin flip:

1. The spinner has 4 areas numbered 1 to 4.
2. The coin has 2 possible outcomes: Heads (H) or Tails (T).

The total number of outcomes is calculated by multiplying the number of spinner outcomes by the number of coin outcomes:

- Outcomes from the spinner: 4 (1, 2, 3, 4)
- Outcomes from the coin: 2 (H, T)

Total outcomes in the sample space = 4 (spinner) × 2 (coin) = 8 outcomes.

The full sample space of outcomes is:
- 1H
- 1T
- 2H
- 2T
- 3H
- 3T
- 4H
- 4T

Now, we need to find the outcomes that are in the event “a number greater than 2.” The numbers greater than 2 from the spinner are 3 and 4. Therefore, the corresponding outcomes based on the coin flips are:

- 3H
- 3T
- 4H
- 4T

So, the event “a number greater than 2” includes:
{3H, 3T, 4H, 4T}

Given the above analysis, the correct response is:

**There are 8 outcomes in the sample space. The event “a number greater than 2” includes {3H, 3T, 4H, 4T}.**