Theoretical and Experimental Probability

Theoretical Probability

First let's review theoretical probability

"what's supposed to happen"

Multiple Choice

So.... theoretical probability is

• how an event is supposed to happen

• what happens after an experiment

• a way of guessing the future

Multiple Select

How can you show the probability of an event? (Choose all that apply)

• fraction

• decimal

• percent

• expression

Multiple Choice

When flipping a coin, what is the theoretical probability of it landing on tails?

p(tails)

• 1

• 2

• 1/2

• 2/1

Multiple Choice

When rolling a number cube, how many total outcomes do you have?

• 2

• 4

• 6

• The limit does not exist

Multiple Choice

What is the theoretical probability of a number cube landing on 5?

• $$\frac{1}{5}$$  

• $$\frac{5}{6}$$  

• $$\frac{1}{6}$$  

• $$1$$  

Multiple Choice

What is the theoretical probability of the arrow landing on blue?

• $$\frac{1}{4}$$

• $$\frac{3}{4}$$

• 4

• 1

Multiple Choice

When you see the word and or or in a probability question, what operation do you have to use?

Ex: P(organges and bananas)

• Add

• Subtract

• Multiply

• Divide

Multiple Choice

A bag contains 9 blue marbles, 10 red marbles, and 11 yellow marbles. What is the probability of randomly choosing a blue or yellow marble from the bag?

• $$\frac{1}{3}$$

• $$\frac{3}{2}$$

• $$\frac{2}{3}$$

• $$\frac{9}{11}$$

Multiple Choice

A bag of candy contains 2 pieces of bubble gum, 4 jolly ranchers, and 10 tootsie rolls.  What is the closest probability of randomly choosing either a piece of bubble gum or a tootsie roll?

• 12.5%

• 25%

• 37.5%

• 75%

Multiple Choice

What is the theoretical probability that Jamya will flip a tails on her next flip of the coin?

• 50%

• 25%

• 33.3%

• 75%

Multiple Choice

A fair number cube has six sides, numbered 1 through 6.  Which of the events has the highest probability of occurring?

• a number less than 3

• an even number

• a number greater than 2

• an odd number

Multiple Choice

What is the probability of picking a pink flower?

• 3/5

• 3/10

• 1/5

• 1/2

​Experimental Probability

So, what's the difference?

• Theoretical probability is what is supposed to happen

• Experimental probability is what actually happens when you do a trial

• If the problem asks you for the experimental probability, look for where the action is! (spinning, rolling, flipping, choosing, etc.)

Multiple Choice

Select the best statement for experimental probability

• The probability of a coin landing on heads

• The probaility of a spinner landing on red

• Spinning an arrow 50 times and landing on green 5 times.

• Having 12 apples and 5 bananas and choosing apples

Multiple Choice

A fair number cube was rolled 40 times. The number 5 was rolled 8 times. What is the experimental probability of rolling the number 5 again?

• $$\frac{1}{6}$$

• $$\frac{1}{5}$$

• 5

• $$\frac{1}{8}$$

Multiple Choice

The arrow of this spinner was spun 10 times and landed on W 7 times. What is the experimental probability of it landing on w?

• $$\frac{7}{10}$$

• $$\frac{1}{4}$$

• $$\frac{1}{10}$$

• $$\frac{1}{7}$$

Multiple Choice

A marble was drawn from the box, recorded on the table, then replaced. This trial was repeated 20 times. What was the experimental probability of drawing a striped marble?

• $$\frac{1}{3}$$

• $$\frac{12}{8}$$

• $$\frac{3}{5}$$

• $$\frac{4}{20}$$

Multiple Choice

One of these tiles was picked out of a bag and replaced 18 times. If the tile E was picked 4 times. What is the experimental probability of picking the E?

• 1/6

• 2/9

• 1/18

• 1/4

Multiple Choice

Use the table to answer this question:

What is the experimental probability of rolling a 5 on a fair number cube?

• 0.0333....

• 0.1666....

• 0.06666....

• 0.2

Multiple Choice

The results of spinning the spinner 42 times are in the table. For which color is the experimental probability the closest to the theoretical probability?

• Red

• Green

• Blue

Multiple Choice

A six-sided cube with sides labeled A through F was rolled 50 times and the results were recorded.

Which of the following is a true statement?

• The theoretical probability of landing on E is less than the experimental probability of landing on B.

• The experimental probability of landing on E is less than the theoretical probability of landing on D.

• The experimental probability of landing on A is more than the theoretical probability of landing on F.

• The theoretical probability of landing on A is more than the experimental probability of landing on C.

Poll

What is the probability of you passing the test next week?

• Certain

• Likely

• Unlikely

• Impossible

We are finished!

You made it to the end!