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Answer :
To determine if the probability model is valid, we need to examine the properties of the given probabilities:
1. Checking if all probabilities are between 0 and 1:
- AP Stats probability: 0.62
- AP Lang. probability: 0.58
- AP Comp. Sci. probability: 0.31
- AP Euro. probability: 0.65
All these probabilities are between 0 and 1, which is a requirement for any valid probability model.
2. Checking if the sum of the probabilities is 1:
- Add up all the probabilities:
[tex]\[
0.62 + 0.58 + 0.31 + 0.65 = 2.16
\][/tex]
The sum of the probabilities is 2.16, which is not equal to 1.
Given these observations, we can conclude:
- The probability model is not valid because the sum of the probabilities is not 1. Although each individual probability is within the valid range (between 0 and 1), the total sum must also equal 1 for the model to be considered valid. Since it is 2.16, the model does not satisfy this criterion.
1. Checking if all probabilities are between 0 and 1:
- AP Stats probability: 0.62
- AP Lang. probability: 0.58
- AP Comp. Sci. probability: 0.31
- AP Euro. probability: 0.65
All these probabilities are between 0 and 1, which is a requirement for any valid probability model.
2. Checking if the sum of the probabilities is 1:
- Add up all the probabilities:
[tex]\[
0.62 + 0.58 + 0.31 + 0.65 = 2.16
\][/tex]
The sum of the probabilities is 2.16, which is not equal to 1.
Given these observations, we can conclude:
- The probability model is not valid because the sum of the probabilities is not 1. Although each individual probability is within the valid range (between 0 and 1), the total sum must also equal 1 for the model to be considered valid. Since it is 2.16, the model does not satisfy this criterion.
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