**Title: Investigating if a Die is Loaded through Probability Experiments**You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the following table. Do you think the die is loaded? Why?| Value of Die | Frequency | Value of Die | Frequency ||--------------|-----------|--------------|-----------|| 1 | 46 | 4 | 45 || 2 | 107 | 5 | 41 || 3 | 40 | 6 | 121 |### Do you think the die is loaded?- **A.** Yes, because two of the values have a higher probability of occurring than expected under the assumption of equally likely outcomes.- **B.** No, because each value has an approximately equal chance of occurring.- **C.** Yes, because the probabilities are not the same.### Explanation:The table above presents the frequency of each face of the die appearing in 400 rolls. Notice how the frequency for certain numbers significantly deviates:- Numbers 2 and 6 appear much more frequently (107 and 121 times, respectively) in comparison to what would be expected with a fair die (approximately 66-67 times each, given 400 rolls).- Other numbers, such as 3, 4, and 5, appear much less frequently, indicating potential bias.Consider these observations when determining whether the die is loaded and select your answer accordingly.

Given: Value of Die Frequency 1 46 2 107 3 40 4 45 5 41 6 121 Now, calculating the probabilities for each value of die. Value of Die Frequency Probability 1 40 0.1 2 41 0.1025 3 45 0.1125 4 46 0.115 5 107 0.2675 6 121 0.3025As, the probabilities for first four values of dice is almost same and for 5 and 6 values of dice the probability is higher. So, the correct option is: Option (A) Yes, because two values have a higher probability of occurring than expected under the assumption of equally likely outcomes.

Math

Statistics

You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the following table. Do you think the die is loaded? Why? Full data setO Value of Die Frequency Value of Die Frequency 1 46 4 45 107 41 3 40 6 121 Do you think the die is loaded? O A. Yes, because two of the values have a higher probability of occurring than expected under the assumption of equally likely outcomes. O B. No, because each value has an approximately equal chance of occurring. OC. Yes, because the probabilities are not the same.

You suspect a 6-sided die to be loaded and conduct a probability experiment by rolling the die 400 times. The outcome of the experiment is listed in the following table. Do you think the die is loaded? Why? Full data setO Value of Die Frequency Value of Die Frequency 1 46 4 45 107 41 3 40 6 121 Do you think the die is loaded? O A. Yes, because two of the values have a higher probability of occurring than expected under the assumption of equally likely outcomes. O B. No, because each value has an approximately equal chance of occurring. OC. Yes, because the probabilities are not the same.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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