To determine which of the given values is not a possible value for a probability, we need to recall the basics of probability. A probability value must lie between 0 and 1, inclusive. This means any number less than 0 or greater than 1 cannot represent a probability.
Let's examine each choice in detail:
- Choice A: [tex]\(\frac{1}{16}\)[/tex]
- By dividing 1 by 16, we get [tex]\(\frac{1}{16} = 0.0625\)[/tex].
- This value is between 0 and 1, so it is a valid probability value.
- Choice B: 0.82
- This value is already given in decimal form.
- Since 0.82 is between 0 and 1, it is a valid probability value.
- Choice C: [tex]\(\frac{10}{100}\)[/tex]
- By dividing 10 by 100, we get [tex]\(\frac{10}{100} = 0.1\)[/tex].
- This value is between 0 and 1, so it is a valid probability value.
- Choice D: 1.001
- This value is already given in decimal form.
- Since 1.001 is greater than 1, it does not lie within our required range of [0, 1].
- Therefore, 1.001 is not a valid probability value.
So, the answer to the question is:
[tex]\[ \boxed{1.001} \][/tex]
This corresponds to choice D, which is the invalid probability value among the given options.
