a spinner has five congruent sections, one each of blue, green, red, orange, and yellow. yuri spins the…

a spinner has five congruent sections, one each of blue, green, red, orange, and yellow. yuri spins the spinner 10 times and records his results in the table.\n| color | number |\n| blue | 1 |\n| green | 2 |\n| red | 0 |\n| orange | 4 |\n| yellow | 3 |\nwhich statements are true about yuris experiment? select three options.\n□ the theoretical probability of spinning any one of the five colors is 20%.\n□ the experimental probability of spinning blue is $\frac{1}{5}$.\n□ the theoretical probability of spinning green is equal to the experimental probability of spinning green.\n□ the experimental probability of spinning yellow is less than the theoretical probability of spinning yellow.\n□ 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.
Answer
Explanation:
Step1: Calculate theoretical probability
The spinner has 5 congruent sections. The theoretical probability of spinning any one - color is $P=\frac{1}{5}=0.2 = 20%$. So the statement "The theoretical probability of spinning any one of the five colors is 20%" is true.
Step2: Calculate experimental probability of blue
The experimental probability of spinning blue is $P_{blue}=\frac{\text{Number of times blue occurred}}{\text{Total number of spins}}=\frac{1}{10}$. So the statement "The experimental probability of spinning blue is $\frac{1}{5}$" is false.
Step3: Calculate theoretical and experimental probability of green
The theoretical probability of spinning green is $\frac{1}{5}=0.2$. The experimental probability of spinning green is $P_{green}=\frac{2}{10}=0.2$. So the statement "The theoretical probability of spinning green is equal to the experimental probability of spinning green" is true.
Step4: Calculate theoretical and experimental probability of yellow
The theoretical probability of spinning yellow is $\frac{1}{5}=0.2$. The experimental probability of spinning yellow is $P_{yellow}=\frac{3}{10}=0.3$. So the statement "The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow" is false.
Step5: Law of large numbers
According to the law of large numbers, as the number of trials increases, the experimental probability gets closer to the theoretical probability. So the statement "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" is true.
Answer:
The theoretical probability of spinning any one of the five colors is 20%; The theoretical probability of spinning green is equal to 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.