Sure, let's look at the problem step-by-step to understand why Sue's answer of [tex]\(\frac{13}{8}\)[/tex] is incorrect.
1. Understand the Concept of Probability:
- The field of probability deals with the likelihood of events occurring.
- The probability of any event ranges from 0 to 1 (inclusive).
- A probability of 0 means the event will definitely not occur.
- A probability of 1 means the event will definitely occur.
- Any probability value between 0 and 1 represents the likelihood of an event occurring.
2. Check Sue's Answer:
- Sue gave an answer of [tex]\(\frac{13}{8}\)[/tex].
3. Convert to Decimal Form:
- [tex]\(\frac{13}{8}\)[/tex] is a fraction. To better understand it, convert it to a decimal.
- Dividing 13 by 8 gives:
[tex]\[
\frac{13}{8} = 1.625
\][/tex]
4. Evaluate the Decimal Result:
- The decimal representation of [tex]\(\frac{13}{8}\)[/tex] is 1.625.
- Recall the valid range for probability values: 0 to 1.
5. Compare to Probability Range:
- 1.625 is greater than 1.
- Since valid probabilities must fall within the range [0, 1], a probability of 1.625 is outside this range.
6. Conclude the Error:
- Because 1.625 is not within the valid range for probability values, Sue realized her answer of [tex]\(\frac{13}{8}\)[/tex] is incorrect.
By following these steps, Sue can explain why her answer does not make sense in the context of probability. The probability value she calculated, 1.625, exceeds the maximum possible value of 1, thereby indicating an error in her computation or reasoning.
