On an exam on probability concepts, Sue had an answer of 13/8 for one problem. Explain how she knew that this result was incorrect.
all probabilities are between 0 and 1
To determine if Sue's answer of 13/8 for a probability problem is incorrect, we need to understand the properties of probabilities. Here are the steps to verify Sue's answer:
Step 1: Understand the probability concept:
Probabilities are represented as fractions or decimals between 0 and 1. A probability of 0 means an event is impossible, and a probability of 1 implies the event is certain to occur.
Step 2: Examine the answer:
Sue's answer of 13/8 indicates a probability greater than 1, which is not possible as probabilities cannot exceed 1. Therefore, it suggests that her answer is incorrect.
Step 3: Simplify the fraction (optional):
If needed, simplify the fraction to its simplest form. In this case, 13/8 cannot be simplified further.
Step 4: Verify the answer:
To confirm Sue's answer, compare the fraction to the given parameters. If the numerator is greater than the denominator, it implies that Sue's answer is incorrect, as it violates the fundamental rule of probability.
In Sue's case, 13/8 violates the fundamental property of probabilities, making it an incorrect answer.
Sue recognized that her answer of 13/8 for a probability problem was incorrect based on her knowledge of probability concepts. Probability can be calculated using a fraction, where the numerator represents the number of favorable outcomes and the denominator represents the total number of possible outcomes.
In probability, the numerator should always be equal to or less than the denominator. This is because the number of favorable outcomes cannot exceed the total number of possible outcomes.
If Sue arrived at an answer of 13/8, it means that she had more favorable outcomes than the total number of possible outcomes, which is not possible. In this case, Sue would have known that her answer was incorrect because it violated the fundamental principle of probability.
To determine the correct answer, Sue could review the problem and make sure she correctly counted the favorable outcomes and the total number of possible outcomes. She could also check her calculations to ensure there were no errors.