Let's go through the questions step-by-step:
### 1. Theoretical Probability of an Unfavorable Outcome
First, we need to determine the theoretical probability of an unfavorable outcome where [tex]\( x \neq 1 \)[/tex].
- The fraction representing the probability of an unfavorable outcome [tex]\( P(x \neq 1) \)[/tex] is:
[tex]\[
\boxed{\frac{5}{6}}
\][/tex]
- To convert this fraction to a percentage, we multiply by 100 and round to the nearest whole number:
[tex]\[
\frac{5}{6} \approx 83 \%
\][/tex]
Thus, the theoretical probability of an unfavorable outcome is:
- [tex]\( P(x \neq 1) \)[/tex]: [tex]\(\boxed{\frac{5}{6}}\)[/tex] (fraction)
- Approximately [tex]\(\boxed{83}\%\)[/tex] (rounded to the nearest percent)
### 2. Exact and Approximate Answers
In the above calculations:
- The exact answer is the fraction:
[tex]\[
\boxed{\text{The fraction }}
\][/tex]
- The approximate answer is the percentage:
[tex]\[
\boxed{83\%}
\][/tex]
### 3. Comparison of Fractions of Total Outcomes and Theoretical Probability
The fractions of the total outcomes and the theoretical probability are the same. Thus, the comparison is:
- The fractions of the total outcomes is the same as the theoretical probability:
[tex]\[
\boxed{\text{True}}
\][/tex]
### 4. Sum of Probabilities of Favorable and Unfavorable Outcomes
Finally, we need to find the sum of the probabilities of favorable and unfavorable outcomes.
- The probability of the favorable outcome [tex]\( P(x = 1) \)[/tex] is:
[tex]\[
\frac{1}{6}
\][/tex]
- The probability of the unfavorable outcome [tex]\( P(x \neq 1) \)[/tex] is:
[tex]\[
\frac{5}{6}
\][/tex]
- Summing these probabilities:
[tex]\[
P(x = 1) + P(x \neq 1) = \frac{1}{6} + \frac{5}{6} = 1.0
\][/tex]
- Converting this to a percentage:
[tex]\[
1.0 \times 100 = 100\%
\][/tex]
Therefore, the sum of the probabilities of the favorable and unfavorable outcomes is:
- [tex]\( \boxed{1.0} \)[/tex]
- Equivalent to [tex]\(\boxed{100}\%\)[/tex]
