To determine whether an answer in probability is correct, we must consider the fundamental properties of probabilities. One of these properties states that a probability value must always fall within the range of 0 to 1, inclusive. This means that a probability cannot be less than 0 or greater than 1.
Sue’s answer to the problem was [tex]\(\frac{13}{8}\)[/tex]. To evaluate the correctness of this answer, let’s follow these steps:
1. Convert the Fraction to a Decimal:
Calculate the value of [tex]\(\frac{13}{8}\)[/tex].
[tex]\[
\frac{13}{8} = 1.625
\][/tex]
2. Verify if the Decimal Lies Within the Valid Probability Range:
Check whether 1.625 falls within the valid range of 0 to 1.
[tex]\[
0 \leq 1.625 \leq 1
\][/tex]
3. Interpret the Result:
Since 1.625 is greater than 1, this value does not satisfy the fundamental property of probabilities. Probabilities exceeding 1 indicate an error in either the calculation, interpretation, or both.
4. Conclusion:
Sue knew that her result was incorrect because a probability value must be between 0 and 1. A result of 1.625 exceeds this range, thereby indicating an error.
Thus, Sue correctly deduced that her answer of [tex]\(\frac{13}{8}\)[/tex] was incorrect because the resulting value of 1.625 falls outside the permissible range for probabilities.
