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Answer :
To determine if the probability model provided is valid, we need to check two main conditions:
1. All probabilities should be between 0 and 1. This ensures that each probability is valid individually.
2. The sum of all probabilities should be 1. This ensures that the probability model accounts for all possible outcomes together.
Let's analyze the given data:
- Probability of passing AP Stats: 0.62
- Probability of passing AP Lang.: 0.58
- Probability of passing AP Comp. Sci.: 0.31
- Probability of passing AP Euro.: 0.65
Step 1: Check Individual Probabilities
Each of these probabilities is between 0 and 1:
- 0.62 is between 0 and 1
- 0.58 is between 0 and 1
- 0.31 is between 0 and 1
- 0.65 is between 0 and 1
Since all individual probabilities are valid, the first condition is satisfied.
Step 2: Calculate the Sum of Probabilities
- Add up all the probabilities: [tex]\(0.62 + 0.58 + 0.31 + 0.65 = 2.16\)[/tex]
The sum of probabilities is 2.16. For a probability model to be valid, this sum should be exactly 1.
Since the sum is not 1, the model does not add up to 100% probability, which indicates that not all possible outcomes are accounted for or that there's an error.
Conclusion:
The probability model is not valid because the sum of the probabilities is not equal to 1.
1. All probabilities should be between 0 and 1. This ensures that each probability is valid individually.
2. The sum of all probabilities should be 1. This ensures that the probability model accounts for all possible outcomes together.
Let's analyze the given data:
- Probability of passing AP Stats: 0.62
- Probability of passing AP Lang.: 0.58
- Probability of passing AP Comp. Sci.: 0.31
- Probability of passing AP Euro.: 0.65
Step 1: Check Individual Probabilities
Each of these probabilities is between 0 and 1:
- 0.62 is between 0 and 1
- 0.58 is between 0 and 1
- 0.31 is between 0 and 1
- 0.65 is between 0 and 1
Since all individual probabilities are valid, the first condition is satisfied.
Step 2: Calculate the Sum of Probabilities
- Add up all the probabilities: [tex]\(0.62 + 0.58 + 0.31 + 0.65 = 2.16\)[/tex]
The sum of probabilities is 2.16. For a probability model to be valid, this sum should be exactly 1.
Since the sum is not 1, the model does not add up to 100% probability, which indicates that not all possible outcomes are accounted for or that there's an error.
Conclusion:
The probability model is not valid because the sum of the probabilities is not equal to 1.
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