Theoretical and Experimental Probability

Theoretical and Experimental Probability

Multiple Choice

Just to review, probability can be written as....

• a fraction

• a percent

• a decimal

• all the above

What is probability?

• Probability is how likely something will occur

• Think of probability of the chance something can or cannot happen

Remember:

Probability is the chance something will happen on a scale from 0 to 1.

How to read the probability scale:

• Impossible (0%): something cannot occur

• Unlikely: there is a small percentage of occurring

• Even Chance (50%): there is a 50% chance it can occur and 50% it cannot

• Likely: there more of a chance something occurring than not

• Certain (100%): it will happen

Multiple Choice

A likely chance event is closer to what number?

• 0

• 0.5

• 1

• 100

Theoretical vs Experimental Probability

Theoretical: is calculating the probability of it happening, what should happen. 
ex. If you flip a coin six times, it should land on heads  $\frac{1}{2}$   , 1 out of 2, or 50% of the time. 

Experimental: is the results of an experiment, what did happen.
ex. you flip and coin and see how many times it lands on heads.

 

Multiple Choice

Experimental Probability is:

• What will happen

• What should happen

• What I think happens

• What does happen

Multiple Choice

Theoretical Probability is:

• What will happen

• What should happen

• What I want to happen

• What does happen

Multiple Choice

What is the theoretical probability of the spinner landing on yellow?

• $$\frac{1}{3}$$

• $$\frac{1}{4}$$

• $$\frac{1}{2}$$

• $$\frac{2}{3}$$

Theoretical Probability

If you and 7 friends were playing Among Us (8 total players) the theoretical probability of being imposter would be  $\frac{1}{8}$  or 12.5%. So, if you played 8 games you would expect to be imposter 1 time.

Experimental Probability

If you played 8 games and were the imposter 3 times then your experimental probability would be  $\frac{3}{8}$  or 37.5%. 

Theoretical and Experimental Probability

- they can be equal or they can be different

In the example before, you were imposter 3 times which is higher than expected of only 1 time. However, you could play 8 games and never be an imposter, thus, having an experimental probability less than the theoretical.

Multiple Choice

Find the theoretical probability of NOT landing on yellow if you spin the spinner.

• $$\frac{1}{8}$$

• $$\frac{7}{8}$$

• 1

• 7

Multiple Choice

Dustin has a spinner that is divided into

5 equal-size sections colored red, blue, orange, white, and green. What is the probability that Dustin spins pink on the next spin?

• 0

• 0.25

• 0.5

• 0.75

Multiple Choice

What is the theoretical probability of randomly picking a Purple marble from Molly's Sack of Marbles?

• $$\frac{4}{5}$$

• $$\frac{3}{15}$$

• $$\frac{2}{15}$$

• $$\frac{8}{21}$$

Multiple Choice

Based on the chart, what is the experimental probability of pulling a green marble?

• 12.5 %

• 8%

• 80%

• 32%

Multiple Choice

The table shows the results of 50 rolls of a number cube. According to the data in the table, what was the experimental probability of rolling a 1? (Simplify if needed)

Multiple Choice

The bar graph shows the results of spinning the spinner 200 times. What is the experimental probability of landing on a 3?

Multiple Choice

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

• As more trials are completed, the experimental probability generally draws closer to the theoretical probability

• As more trials are completed, the theoretical probability generally draws closer to the experimental probability