https://file.aiquickdraw.com/mathbot/file/1728002447347nv80mn0m.jpg

Let's break down the questions and work through them based on the provided image:

### (a) Experimental Probability:
You are asked to find the **experimental probability** of selecting either the ball 1 or ball 2 *and* drawing a card that is either Q or J. 

1. First, identify the outcomes that involve ball 1 or 2:
   - 1Q: 10 trials
   - 1J: 17 trials
   - 2Q: 20 trials
   - 2J: 16 trials

   Add up these values:
   \[
   10 + 17 + 20 + 16 = 63 \text{ trials}
   \]

2. There were a total of **120 trials**, so the experimental probability is:
   \[
   P(\text{experimental}) = \frac{63}{120} = 0.525
   \]

### (b) Theoretical Probability:
Now, find the **theoretical probability** of the same event. 

1. There are **3 balls** and **3 cards**, so the total number of possible outcomes is:
   \[
   3 \times 3 = 9 \text{ outcomes}
   \]

2. Outcomes where either ball 1 or 2 is selected and the card is Q or J:
   - 1Q, 1J, 2Q, 2J (4 outcomes)

3. The probability is:
   \[
   P(\text{theoretical}) = \frac{4}{9} \approx 0.444
   \]

### (c) True Statement:
Comparing the two probabilities:
- The **experimental probability** is \(0.525\).
- The **theoretical probability** is \(0.444\).

Looking at the answer options:
- The first option is the correct one: "With a small number of trials, it is surprising when the experimental probability is much greater than the theoretical probability."

Would you like more details or further explanations?

### Related Questions:
1. How is experimental probability different from theoretical probability?
2. What factors might cause discrepancies between experimental and theoretical probabilities?
3. How could we improve the accuracy of experimental probability?
4. What assumptions are made in calculating theoretical probability?
5. How would the experimental probability change if we increased the number of trials?

### Tip:
To improve experimental accuracy, it's important to increase the number of trials, which makes the experimental probability converge to the theoretical value.

There is a bag with three balls numbered 1 to 3 and a pack of three cards labeled K, Q, and J. In 120 trials, the ball and card were randomly selected, and the results were recorded. Calculate the experimental and theoretical probabilities for selecting ball 1 or 2 and card Q or J, and choose the correct statement based on these probabilities.

Learn how to calculate experimental and theoretical probabilities in a trial involving random selection of balls and cards. In this example, you will calculate probabilities based on 120 trials where a ball and a card are drawn from separate sets. This problem focuses on core probability concepts suitable for high school students.

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