To determine which statements about Yuri's experiment are true, let's analyze the information step-by-step in detail.
1. Theoretical Probability of Spinning Any One of the Five Colors:
- Since the spinner has five congruent sections, the probability of landing on any one color for a single spin is:
[tex]\[
\text{Theoretical Probability} = \frac{1}{5} = 0.2 = 20\%
\][/tex]
So, the first statement is true.
2. Experimental Probability of Spinning Blue:
- Yuri's results show that blue came up 1 time out of 10 spins.
- The experimental probability of spinning blue is:
[tex]\[
\text{Experimental Probability (Blue)} = \frac{\text{Number of Blue Spins}}{\text{Total Spins}} = \frac{1}{10} = 0.1
\][/tex]
- Comparing this with the statement [tex]\(\frac{1}{5}\)[/tex], which is 0.2, we see that 0.1 is not equal to 0.2.
Therefore, the second statement is false.
3. Theoretical Probability of Spinning Green Equals Experimental Probability of Spinning Green:
- The theoretical probability of landing on green is the same as any other color:
[tex]\[
\text{Theoretical Probability (Green)} = \frac{1}{5} = 0.2
\][/tex]
- Yuri's results show that green came up 2 times out of 10 spins:
[tex]\[
\text{Experimental Probability (Green)} = \frac{\text{Number of Green Spins}}{\text{Total Spins}} = \frac{2}{10} = 0.2
\][/tex]
- Since the theoretical and experimental probabilities are both 0.2, the third statement is true.
4. Experimental Probability of Spinning Yellow is Less Than Theoretical Probability of Spinning Yellow:
- The theoretical probability of landing on yellow is:
[tex]\[
\text{Theoretical Probability (Yellow)} = \frac{1}{5} = 0.2
\][/tex]
- Yuri's results show that yellow came up 3 times out of 10 spins:
[tex]\[
\text{Experimental Probability (Yellow)} = \frac{\text{Number of Yellow Spins}}{\text{Total Spins}} = \frac{3}{10} = 0.3
\][/tex]
- Comparing 0.3 to 0.2, we see that 0.3 is not less than 0.2.
Therefore, the fourth statement is false.
5. Law of Large Numbers and Spinning Orange:
- According to the law of large numbers, as the number of trials increases, the experimental probability tends to get closer to the theoretical probability.
- If Yuri spins the spinner 600 more times, the experimental probability of spinning orange should approach the theoretical probability of [tex]\(0.2\)[/tex]:
[tex]\[
\text{Theoretical Probability (Orange)} = 0.2 \quad \text{because each section is congruent}.
\][/tex]
Therefore, the fifth statement is true.
Given this analysis, the three correct statements are:
- The theoretical probability of spinning any one of the five colors is [tex]\(20\%\)[/tex].
- The theoretical probability of spinning green equals the experimental probability of spinning green.
- If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.
