Answer :
To determine which numbers cannot be probabilities, we need to recall the definition of probability. A probability must be a value between 0 and 1, inclusive. Therefore, any number less than 0 or greater than 1 cannot be a probability.
Let's analyze each of the given numbers:
1. -0.00001: This number is less than 0. Since probabilities cannot be negative, -0.00001 cannot be a probability.
2. 0.5: This number is within the range of 0 and 1 (inclusive). Hence, 0.5 is a valid probability.
3. 1.001: This number is greater than 1. Since probabilities cannot exceed 1, 1.001 cannot be a probability.
4. 20%: This is a percentage, which must be converted to a decimal to interpret as a probability. To convert a percentage to a decimal, divide by 100. Thus, 20% is equivalent to 0.20. Since 0.20 is within the range of 0 and 1 (inclusive), it is a valid probability.
Summarizing the analysis:
- -0.00001 and 1.001 cannot be probabilities because they fall outside the range of 0 to 1.
Therefore, the numbers that cannot be probabilities are:
[tex]$[-0.00001, 1.001]$[/tex]
Let's analyze each of the given numbers:
1. -0.00001: This number is less than 0. Since probabilities cannot be negative, -0.00001 cannot be a probability.
2. 0.5: This number is within the range of 0 and 1 (inclusive). Hence, 0.5 is a valid probability.
3. 1.001: This number is greater than 1. Since probabilities cannot exceed 1, 1.001 cannot be a probability.
4. 20%: This is a percentage, which must be converted to a decimal to interpret as a probability. To convert a percentage to a decimal, divide by 100. Thus, 20% is equivalent to 0.20. Since 0.20 is within the range of 0 and 1 (inclusive), it is a valid probability.
Summarizing the analysis:
- -0.00001 and 1.001 cannot be probabilities because they fall outside the range of 0 to 1.
Therefore, the numbers that cannot be probabilities are:
[tex]$[-0.00001, 1.001]$[/tex]