It looks like you've uploaded two images related to a probability problem. The first one presents an experiment involving drawing a card and flipping a coin, and the second image includes a few questions about experimental and theoretical probabilities.

Let's break it down:

Part (a)

We need to use the data provided in the first image to find the experimental probability for drawing the "2 card" and flipping heads in a single trial.

From the table in the first image:

• Outcome 1H (drawing the "1 card" and flipping heads) has 10 trials.
• Outcome 2H (drawing the "2 card" and flipping heads) has 18 trials.
• Outcome 3H (drawing the "3 card" and flipping heads) has 18 trials.
• Outcome 4H (drawing the "4 card" and flipping heads) has 17 trials.
• Total trials = 110.

The experimental probability for drawing the 2 card and flipping heads is:

$P(\text{2 and heads}) = \frac{\text{Number of trials for 2H}}{\text{Total trials}} = \frac{18}{110} = 0.1636$

Part (b)

Now, for the theoretical probability, assuming the card is chosen at random and the coin is fair, we calculate the probability for both drawing the "2 card" and flipping heads.

• The probability of drawing the 2 card from the 4 cards is $P(\text{drawing the 2 card}) = \frac{1}{4}$.
• The probability of flipping heads from a fair coin is $P(\text{flipping heads}) = \frac{1}{2}$.

So, the theoretical probability for drawing the 2 card and flipping heads is:

$P(\text{2 and heads}) = P(\text{drawing the 2 card}) \times P(\text{flipping heads}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8} = 0.125$

Part (c)

For the multiple-choice question, let's consider the truth of the statement regarding the experimental and theoretical probabilities:

• The experimental probability is based on data from actual trials.
• The theoretical probability is based on expected outcomes in an ideal scenario.

The correct answer will likely be:

"The experimental and theoretical probabilities are close, but they might not be equal."

Would you like further explanation or clarification on any of the parts?

Related Questions:

1. How do you calculate experimental probability with other data sets?
2. What is the difference between experimental and theoretical probabilities?
3. How can you improve the accuracy of experimental probability?
4. What is the significance of the law of large numbers in experimental probability?
5. How would you adjust the probability calculation if the card deck or coin were modified?

Tip: Remember that experimental probability can vary from the theoretical probability, especially with a smaller number of trials, but they should converge as the number of trials increases!