To determine whether Derick's statement about the probability of a plastic water bottle landing upright is correct, we need to review the fundamental concept of probability.
1. Understanding Probability:
- Probability measures the likelihood of an event occurring.
- It's expressed as a number between 0 and 1 (inclusive), where:
- 0 indicates an event that will not happen.
- 1 indicates an event that will definitely happen.
- Probabilities cannot be negative or exceed 1.
2. Analyzing Derick's Statement:
- Derick claims that the probability of the water bottle landing upright is 1.2.
- This value (1.2) is greater than 1.
3. Evaluating the Validity:
- Since valid probability values must be within the range [0, 1], a value of 1.2 is invalid.
- Therefore, Derick's statement is incorrect because 1.2 is not within the valid probability range.
Let's evaluate the given choices in light of this understanding:
1. Derick is incorrect because probability is a number from 0 to 1.
- This statement is accurate. Since probabilities range from 0 to 1, Derick's statement of 1.2 is not valid.
2. Derick is correct because probability is always a positive number.
- While it is true that probabilities are positive, they must also be less than or equal to 1. Thus, this statement does not validate Derick's incorrect probability.
3. Derick is correct because [tex]$1.2 > 1$[/tex].
- This statement misunderstands the nature of probabilities. Being greater than 1 does not make Derick correct about the probability; it actually confirms that the value is invalid.
4. Derick is incorrect because [tex]$1.2 > 0$[/tex].
- While 1.2 is indeed greater than 0, this reasoning is not sufficient to demonstrate why Derick's statement is incorrect. The error in Derick's statement is primarily because the value exceeds 1, not merely because it is greater than 0.
Therefore, the correct statement is:
Derick is incorrect because probability is a number from 0 to 1.
