Question 1201209: a)Suppose a randomly selected passenger is about to go through the metal detector at LAX.
Consider the following two outcomes: the passenger sets off the metal detector and the passenger does not set off the metal detector. If you are to find the probability of these two outcomes, would you use the classical approach or the relative frequency approach? Explain why.
b) The coach of a college football team thinks there is .75 probability that the team will win the national championship this year. Is this the case of classical, relative frequency or subjective probability? Explain why.
Answer by asinus(45)   (Show Source):
You can put this solution on YOUR website! Let's address each part of the question step by step.
### Part a: Probability of Setting Off the Metal Detector
**Question:** Would you use the classical approach or the relative frequency approach to find the probability of a passenger setting off the metal detector?
**Answer:**
In this scenario, the appropriate approach to use would be the **relative frequency approach**.
**Explanation:**
- The classical approach is typically used when the outcomes are equally likely and can be determined through theoretical reasoning (e.g., rolling a fair die).
- In the case of the metal detector, we do not have a theoretical basis for determining the exact probabilities of a passenger setting off the detector or not. Instead, we would rely on historical data or empirical evidence from past occurrences (e.g., how many passengers set off the detector versus how many did not) to estimate these probabilities.
- Therefore, since we would be using observed data to calculate the probabilities, the relative frequency approach is more suitable.
### Part b: Probability of Winning the National Championship
**Question:** Is the coach's belief that there is a 0.75 probability that the team will win the national championship an example of classical, relative frequency, or subjective probability?
**Answer:**
This case represents **subjective probability**.
**Explanation:**
- Subjective probability is based on personal judgment, intuition, or belief rather than on objective data or statistical analysis. It reflects an individual's opinion about the likelihood of an event occurring.
- In this case, the coach's estimate of a 0.75 probability that the team will win the national championship is based on their personal assessment of the team's capabilities, performance, and other factors, rather than on a mathematical model or historical frequency data.
- Therefore, since the probability is derived from the coach's beliefs and not from empirical data or theoretical reasoning, it is classified as subjective probability.
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