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Calculate the theoretical probability.
Karl can choose from a solid, plaid, or striped tie to go with three colors of shirts: white, blue, and gray. What is the probability that Karl chooses
a striped tie and a white shirt? Round to the nearest tenth as needed.
Enter the correct value in the box.
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Verified Answer :

GinnyAnswer

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.
\(\[ \text{Total Combinations} = 3 \text{ (ties)} \times 3 \text{ (shirts)} = 9 \]\)

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.
\(\[ \text{Probability (\%)} = \left( \frac{1 \text{ (desired combination)}}{9 \text{ (total combinations)}} \right) \times 100 \approx 11.1111 \% \]\)

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 \(\( \boxed{11.1\%} \)\).

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