Let's solve the problem step-by-step.
1. Identify the Options:
- Karl has 3 choices of ties: solid, plaid, and striped.
- Karl has 3 choices of shirts: white, blue, and gray.
2. Calculate the Total Number of Combinations:
To find the total number of possible combinations of ties and shirts, we multiply the number of tie options by the number of shirt options.
[tex]\[
\text{Total Combinations} = 3 \text{ (ties)} \times 3 \text{ (shirts)} = 9
\][/tex]
3. Determine the Desired Combination:
We are looking for the combination of a striped tie and a white shirt. There is only 1 such specific combination.
4. Calculate the Theoretical Probability:
The probability is given by the number of desired combinations divided by the total number of combinations, multiplied by 100 to convert it to a percentage.
[tex]\[
\text{Probability (\%)} = \left( \frac{1 \text{ (desired combination)}}{9 \text{ (total combinations)}} \right) \times 100 \approx 11.1111 \%
\][/tex]
5. Round the Probability to the Nearest Tenth:
When rounding 11.1111 to the nearest tenth, we obtain 11.1%.
Therefore, the theoretical probability that Karl chooses a striped tie and a white shirt is [tex]\( \boxed{11.1\%} \)[/tex].
