Answer :
To determine which of the given values is not a possible value for a probability, we need to remember that a probability must lie between 0 and 1, inclusive. This means the value of probability can be 0, any fraction or decimal between 0 and 1, or 1.
Now, let's evaluate each of the given options:
Option A: [tex]\(\frac{1}{10}\)[/tex]
[tex]\(\frac{1}{10}\)[/tex] can be converted to a decimal:
[tex]\[ \frac{1}{10} = 0.1 \][/tex]
0.1 lies between 0 and 1, so [tex]\(\frac{1}{10}\)[/tex] is a valid probability.
Option B: [tex]\(\frac{11}{10}\)[/tex]
[tex]\(\frac{11}{10}\)[/tex] can be converted to a decimal:
[tex]\[ \frac{11}{10} = 1.1 \][/tex]
1.1 is greater than 1, so [tex]\(\frac{11}{10}\)[/tex] is not a valid probability.
Option C: [tex]\(\frac{1}{16}\)[/tex]
[tex]\(\frac{1}{16}\)[/tex] can be converted to a decimal:
[tex]\[ \frac{1}{16} = 0.0625 \][/tex]
0.0625 lies between 0 and 1, so [tex]\(\frac{1}{16}\)[/tex] is a valid probability.
Option D: 0.001
0.001 is already in decimal form and it lies between 0 and 1, so 0.001 is a valid probability.
From our analysis, we determine that [tex]\(\frac{11}{10}\)[/tex] or 1.1 is not a valid probability, as it is greater than 1.
Therefore, the answer is:
B. [tex]\(\frac{11}{10}\)[/tex]
Now, let's evaluate each of the given options:
Option A: [tex]\(\frac{1}{10}\)[/tex]
[tex]\(\frac{1}{10}\)[/tex] can be converted to a decimal:
[tex]\[ \frac{1}{10} = 0.1 \][/tex]
0.1 lies between 0 and 1, so [tex]\(\frac{1}{10}\)[/tex] is a valid probability.
Option B: [tex]\(\frac{11}{10}\)[/tex]
[tex]\(\frac{11}{10}\)[/tex] can be converted to a decimal:
[tex]\[ \frac{11}{10} = 1.1 \][/tex]
1.1 is greater than 1, so [tex]\(\frac{11}{10}\)[/tex] is not a valid probability.
Option C: [tex]\(\frac{1}{16}\)[/tex]
[tex]\(\frac{1}{16}\)[/tex] can be converted to a decimal:
[tex]\[ \frac{1}{16} = 0.0625 \][/tex]
0.0625 lies between 0 and 1, so [tex]\(\frac{1}{16}\)[/tex] is a valid probability.
Option D: 0.001
0.001 is already in decimal form and it lies between 0 and 1, so 0.001 is a valid probability.
From our analysis, we determine that [tex]\(\frac{11}{10}\)[/tex] or 1.1 is not a valid probability, as it is greater than 1.
Therefore, the answer is:
B. [tex]\(\frac{11}{10}\)[/tex]
