Understanding Theoretical and Experimental Probability

What does theoretical probability represent?

• The outcome of a single random experiment

• The percentage of times an event occurs over a long period

• The ratio of favorable outcomes to total possible outcomes

• The likelihood of an event based on actual experiments

What is the theoretical probability of landing on yellow with a fair spinner divided into five equal sections?

• 10%

• 25%

• 20%

• 50%

How does experimental probability differ from theoretical probability?

• It is always more accurate than theoretical probability

• It is a theoretical calculation not based on actual data

• It does not consider the total number of possible outcomes

• It is based on the actual outcomes of an experiment

After 200 spins, how many times would we expect the spinner to land on red according to theoretical probability?

• 40 times

• 60 times

• 50 times

• 100 times

What trend is observed as the number of trials in an experiment increases?

• The experimental probability deviates more from the theoretical probability

• The experimental probability becomes less predictable

• The number of outcomes decreases

• The experimental probability tends to match the theoretical probability more closely

What is relative frequency in the context of probability?

• The difference between theoretical and experimental probability

• A method to calculate theoretical probability

• The ratio of the number of times an event occurs to the total number of trials

• The frequency of the most common outcome in an experiment

If a spinner is divided into eight equal sections, what is the theoretical probability of landing on a section colored yellow?

• 12.5%

• 25%

• 10%

• 20%

How many times would you expect the spinner to land on yellow after 4,800 spins?

• 600 times

• 400 times

• 1,200 times

• 800 times

In the final experiment, how many times is the spinner expected to stop on blue out of 4,800 spins?

• 1,600 times

• 1,200 times

• 1,800 times

• 2,000 times

What does the close match between experimental and theoretical probabilities after many trials demonstrate?

• The inaccuracy of theoretical probability

• The unpredictability of random events

• The law of large numbers

• The failure of experimental methods