Theoretical and experimental probability.

If a bag contains 3 red marbles, 2 blue marbles, and 5 green marbles, what is the theoretical probability of drawing a blue marble in a single attempt?

• 2

A die is rolled 60 times, and the number 4 appears 12 times. What is the experimental probability of rolling a 4?

• 25%

• 20%

What usually happens to experimental probability as we increase the number of trials?

• It moves away from theoretical probability.

• It remains completely random.

• It gets closer to theoretical probability.

• It depends on the type of experiment; sometimes it moves closer, other times it moves away.

Answer explanation

Imagine you are flipping a coin. We know that, in theory, the probability of getting heads is 50% (or 1/2) because there are only two possible outcomes: heads or tails.

But what happens if you flip the coin just 5 times? You might get heads 3 times and tails 2 times, which is not exactly 50%. That’s because with just a few flips, results can be random.

Now, what if you flip the coin 1,000 times? The number of heads and tails will likely be much closer to 50% each.

This is what the Law of Large Numbers tells us: The more times we repeat an experiment, the closer the experimental probability gets to the theoretical probability.

So, if we roll a die, pick cards, or spin a wheel many, many times, the results will start to match what we expect mathematically!

In a lottery game where you have to guess five numbers, what type of probability is used to calculate the chances of winning before playing?

• Experimental probability.

• Theoretical probability.

• Subjective probability.

• Conditional probability.

Which of the following statements best differentiates theoretical probability from experimental probability?

• Experimental probability is calculated before conducting an experiment, and theoretical probability is determined afterward.

• Theoretical probability is based on opinions and past experiences, while experimental probability is a mathematical formula.

• Theoretical probability is based on mathematical calculations, while experimental probability depends on the observation of real results.

• There is no difference; both depend on the number of times an event occurs.

If you flip a coin 100 times and get heads 42 times, is the experimental probability of getting heads the same as the theoretical probability? Explain why they might be different.

After watching the video and answering the questions, explain in your own words what you understood about theoretical and experimental probability. What was the most important idea you understood? What questions or doubts do you still have about the topic?