Example problem illustrating the difference between experimental and theoretical probability with a card drawing scenario.

Problem Analysis:

The problem involves comparing the experimental probability and the theoretical probability of drawing the Queen of Hearts from a standard 52-card deck. Here's a breakdown of the task:

1. Experimental Probability: This is calculated based on the results of an experiment. In this case, a card is drawn and replaced 200 times, and the Queen of Hearts is drawn 5 times.
- Formula:
\[
\text{Experimental Probability} = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}
\]

2. Theoretical Probability: This is calculated based on the inherent properties of the deck. Since there is only one Queen of Hearts in a standard 52-card deck, the probability of drawing it in a single draw is:
- Formula:
\[
\text{Theoretical Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\]

3. Comparison: We need to determine which probability (experimental or theoretical) is higher.

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Step-by-Step Solution:

#### 1. Calculate the Experimental Probability:
- The event of interest is drawing the Queen of Hearts.
- The number of times this event occurred is 5.
- The total number of trials is 200.
- Using the formula for experimental probability:
\[
\text{Experimental Probability} = \frac{5}{200} = 0.025
\]
- Convert to a percentage:
\[
0.025 \times 100 = 2.5\%
\]

#### 2. Calculate the Theoretical Probability:
- There is only 1 Queen of Hearts in a standard 52-card deck.
- The total number of possible outcomes when drawing a card is 52.
- Using the formula for theoretical probability:
\[
\text{Theoretical Probability} = \frac{1}{52}
\]
- Approximate the value:
\[
\frac{1}{52} \approx 0.01923
\]
- Convert to a percentage:
\[
0.01923 \times 100 \approx 1.923\%
\]

#### 3. Compare the Probabilities:
- Experimental Probability: \( 0.025 \) (or 2.5%)
- Theoretical Probability: \( \approx 0.01923 \) (or 1.923%)

Clearly, the experimental probability (\( 0.025 \)) is higher than the theoretical probability (\( \approx 0.01923 \)).

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Final Answer:

\[
\boxed{\text{Experimental Probability is higher}}
\]