Math Problem Statement
Solution
Let's go through the problem step by step.
(a) Experimental Probability of Landing on Red
The experimental probability is calculated by dividing the number of times the red slice was landed on by the total number of spins.
From the table:
- Number of red spins = 187
- Total number of spins = 500
So, the experimental probability of landing on red is: Rounded to the nearest thousandth: 0.374.
(b) Theoretical Probability of Landing on Red
To compute the theoretical probability, we need to consider the number of red slices compared to the total number of slices. The spinner has:
- 4 red slices,
- 4 yellow slices,
- 2 blue slices.
The total number of slices is . The theoretical probability of landing on red is: So, the theoretical probability of landing on red is 0.4.
(c) Choosing the Correct Statement
The law of large numbers states that as the number of trials (spins) increases, the experimental probability tends to get closer to the theoretical probability. Hence, the correct statement is:
- The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
Would you like any further details or explanations on these concepts?
Here are 5 related questions to extend your understanding:
- How do you calculate the experimental probability for yellow or blue slices?
- What factors can affect experimental probability in real-world situations?
- Why is theoretical probability always based on the assumption of fairness in the spinner?
- How would the probabilities change if the spinner had 12 slices instead of 10?
- What happens to the experimental probability if we increase the number of spins significantly, say to 5000?
Tip: Always compare experimental probability with theoretical probability to check for consistency in real-world experiments!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Experimental Probability
Theoretical Probability
Law of Large Numbers
Formulas
P(Event) = Number of favorable outcomes / Total number of outcomes
Theorems
Law of Large Numbers
Suitable Grade Level
Grades 6-8
Related Recommendation
Theoretical and Experimental Probability of Spinner Outcomes
Calculating the Probability of Not Landing on Red: A Spinner Problem
Theoretical Probability of Landing on Red in a Spinner
Theoretical and Experimental Probability: Spinner Results Analysis
Comparing Theoretical and Experimental Probabilities of a Spinner