Question

There is a spinner with 20 equally likely sections, numbered from 1 to 20. You have the opportunity to spin it. If the number is odd, you win $10. If the number is even, you win nothing. X is the payoff for playing the game. Write the probability distribution of X in the table to the right. Which probability is correct for the blanks.
(1 Point)


0.5

0.004

0.996

0.95

Answer 1

Let's analyze the situation with the spinner and determine the probability distribution of the payoff \( X \).

1. **Understanding the Game:**
- There are 20 sections on the spinner numbered from 1 to 20.
- Odd numbers (1, 3, 5, ..., 19) result in a win of $10.
- Even numbers (2, 4, 6, ..., 20) result in winning nothing ($0).

2. **Counting Odds and Evens:**
- There are 10 odd numbers: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}.
- There are 10 even numbers: {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}.

3. **Calculating Probabilities:**
- Probability of winning $10 (by spinning an odd number):
\[
P(X = 10) = \frac{10}{20} = 0.5
\]
- Probability of winning $0 (by spinning an even number):
\[
P(X = 0) = \frac{10}{20} = 0.5
\]

4. **Probability Distribution Table:**
- Payoff \( X \): Possible outcomes are either $0 or $10.
- The probabilities we calculated lead to the following probability distribution:

| X | P(X) |
|-------|------|
| 0 | 0.5 |
| 10 | 0.5 |

5. **Choices Given:**
- The provided probabilities are:
- 0.5
- 0.004
- 0.996
- 0.95

The correct probability for the blanks in the context of the payoff distribution derived above is **0.5** for both \( P(X = 0) \) and \( P(X = 10) \).

Therefore, the correct answer is **0.5**.