Theoretical vs Experimental Probability

The video tutorial explains the difference between theoretical and experimental probability. It uses examples like coin flips and a spinner problem to illustrate how theoretical probability is calculated and how experimental probability is observed. The tutorial highlights that with a small number of trials, experimental results can vary widely from theoretical predictions, but with more trials, results tend to align more closely with theoretical probability.

What is the main difference between theoretical and experimental probability?

• Experimental probability is always more accurate than theoretical probability.

• Theoretical probability always matches experimental probability.

• Theoretical probability is calculated mathematically, while experimental probability is based on real-world trials.

• Theoretical probability is based on actual experiments, while experimental probability is based on calculations.

In a theoretical probability scenario, what is the expected outcome of flipping a fair coin four times?

• Two heads and two tails

• Four tails

• Four heads

• Three heads and one tail

Why do experimental probabilities often differ from theoretical probabilities?

• Because theoretical probabilities are based on biased assumptions.

• Because experimental probabilities are calculated using different formulas.

• Because experimental probabilities are based on random real-world events.

• Because theoretical probabilities are always incorrect.

What happens to experimental probability as the number of trials increases?

• It remains unchanged.

• It gets closer to the theoretical probability.

• It diverges further from theoretical probability.

• It becomes less accurate.

In the spinner problem, what is the theoretical probability of landing on black or grey?

• 0.75

• 0.25

• 1.0

• 0.5

How is the theoretical probability of landing on black or grey expressed as a decimal?

• 0.75

• 0.50

• 1.00

• 0.25

What is the experimental probability of landing on black or grey based on Jane's results?

• 0.60

• 0.50

• 0.40

• 0.25

How do the theoretical and experimental probabilities compare in Jane's spinner experiment?

• The experimental probability is higher.

• They are completely unrelated.

• They are exactly the same.

• The theoretical probability is higher.

Which statement is true regarding a small number of trials in probability experiments?

• Theoretical probability is always more accurate.

• Experimental probability can vary widely from theoretical probability.

• Experimental probability will always be less than theoretical probability.

• Experimental probability is always more accurate.

What is the relationship between the number of trials and the accuracy of experimental probability?

• The number of trials does not affect accuracy.

• More trials lead to more accuracy.

• Fewer trials lead to more accuracy.

• More trials lead to less accuracy.