Asked by serenity
The spinner below shows
5
equally sized slices. Debra spun the dial
50
times and got the following results.
OutcomeWhiteGreyBlackNumber of Spins
20
19
11
Fill in the table below. Round your answers to the nearest thousandth.
(a)From Debra's results, compute the experimental probability of landing on black.
(b)Assuming that the spinner is fair, compute the theoretical probability of landing on black.
(c)Assuming that the spinner is fair, choose the statement below that is true:
As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
The experimental and theoretical probabilities must always be equal.
As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.
5
equally sized slices. Debra spun the dial
50
times and got the following results.
OutcomeWhiteGreyBlackNumber of Spins
20
19
11
Fill in the table below. Round your answers to the nearest thousandth.
(a)From Debra's results, compute the experimental probability of landing on black.
(b)Assuming that the spinner is fair, compute the theoretical probability of landing on black.
(c)Assuming that the spinner is fair, choose the statement below that is true:
As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
The experimental and theoretical probabilities must always be equal.
As the number of spins increases, we expect the experimental and theoretical probabilities to become farther apart.
Answers
Answered by
GPT-4o mini
Let's break down your questions step by step.
### (a) Experimental Probability of Landing on Black
To calculate the experimental probability, you can use the formula:
\[
\text{Experimental Probability} = \frac{\text{Number of Spins for the Outcome}}{\text{Total Number of Spins}}
\]
In this case, the number of spins for black is 11, and the total number of spins is 50. So:
\[
\text{Experimental Probability of Black} = \frac{11}{50} = 0.22
\]
Rounding to the nearest thousandth, the experimental probability of landing on black is **0.220**.
### (b) Theoretical Probability of Landing on Black
Since the spinner has 5 equally sized slices, and assuming it is fair, the theoretical probability can be calculated as:
\[
\text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{5} = 0.2
\]
### (c) True Statement About Experimental vs. Theoretical Probabilities
The correct statement is:
**As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.**
This reflects the Law of Large Numbers, which states that as you conduct more trials, the experimental probabilities will converge to the theoretical probabilities.
### (a) Experimental Probability of Landing on Black
To calculate the experimental probability, you can use the formula:
\[
\text{Experimental Probability} = \frac{\text{Number of Spins for the Outcome}}{\text{Total Number of Spins}}
\]
In this case, the number of spins for black is 11, and the total number of spins is 50. So:
\[
\text{Experimental Probability of Black} = \frac{11}{50} = 0.22
\]
Rounding to the nearest thousandth, the experimental probability of landing on black is **0.220**.
### (b) Theoretical Probability of Landing on Black
Since the spinner has 5 equally sized slices, and assuming it is fair, the theoretical probability can be calculated as:
\[
\text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{5} = 0.2
\]
### (c) True Statement About Experimental vs. Theoretical Probabilities
The correct statement is:
**As the number of spins increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.**
This reflects the Law of Large Numbers, which states that as you conduct more trials, the experimental probabilities will converge to the theoretical probabilities.