Theoretical and Experimental Probability

Theoretical and Experimental Probability

In class on Tuesday, we learned probability of simple events

• Rolling a 1 on a dice is 1/6, Rolling an even number on a dice is 3/6

• Flipping a coin and landing on heads is 1/2

• You can make predictions by multiplying your probability by the number of trials you are doing in an experiment.

• How many times will you roll a number 5 out of 600 trials?

• 1/6 times 600=100

• So out of 600 rolls, you should get a 5, 100 times.

Multiple Choice

What is the theoretical probability of rolling a 5 on a dice?

• 1/6

• 5/6

• 6

• 15

Multiple Choice

Theoretically, what is the probability that you will land on a 3?

• 25%

• 50%

• 75%

• 0%

Multiple Choice

Dan has 5 pencils and 7 pens in his bag. What is the theoretical probability of pulling out a pencil? 

• 5/7
• 5/12
• 7/12
• 7/5

Multiple Choice

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

• 1/8
• 7/8
• 1
• 7

Multiple Choice

An experiment consists of rolling a fair number cube. Find the theoretical probability of rolling a 3.

• 1/6
• 3/6
• 1
• 1/2

Multiple Choice

What is Theoretical Probability?

• The ratio of favorable outcomes to the total number of possible outcomes
• The ratio of favorable outcomes to the total number of trials in an experiment
• In probability, a controlled, repeated process (such as repeatedly tossing a coin).
• A single possible result.

Multiple Choice

  Which of the following describes theoretical probability?

• a.  Perform an experiment to determine the probability
• a.      Determining the expected probability of an event
• a.  Perform a simulation and count the number of possible outcomes
• a.  Use trials to count the number of desired outcomes

Multiple Choice

What is the theoretical probability of picking a vowel from the letters A, B, C, D, and E?

• 2/5
• 2/3
• 1/5
• 25%

Multiple Choice

McKayla flipped a coin 150 times. How many times could McKayla expect the coin to land on tails?

• 25

• 50

• 75

• 100

Multiple Choice

Achilles rolled a number cube, labeled 1 through 6, 200 times and recorded each of his results. About how many times could Achilles expect to roll a 3 or 4?

• 35

• 70

• 100

• 130

Multiple Choice

Bella will roll a number cube, labeled 1 through 6, 300 times. About how many times could Bella expect to roll a number less than 4?

• 50

• 100

• 150

• 200

THE MORE TRIALS YOU DO, THE CLOSER THE THEORETICAL PROBABILITY IS TO THE EXPERIMENTAL PROBABILITY

• increase trials for more accuracy!

• More trials=more validity

Multiple Choice

 Josh is rolling dice in a probability experiment. If Josh wants the experimental probability to be as close as possible to the theoretical probability, which plan should he use?

• Roll 4 times
• Roll 40 times
• Roll 75 times
• Roll 140 times

Multiple Choice

A coin is tossed 18 times. It lands on heads 12 times. What is the experimental probability of the coin landing on tails? reduce the fraction!

Multiple Choice

Experimental Probability is ______

• data from our experiment

• our prediction

Multiple Choice

What is the difference between theoretical and experimental probability?

• Experimental Probability is what should happen while Theoretical Probability is what does happen.

• Theoretical Probability is what should happen while Experimental Probability is what does happen.

• There is no difference.

• One is a fraction and one is a decimal.

Multiple Choice

Jason rolls a die 14 times. What is the Experimental probability that he will roll a 2 ?

• 2/6

• 3/6

• 3/14

• 1/6

Multiple Choice

Shannon has a bag of jelly beans. She removed one jelly bean, recording the color, and then replaced it. She repeated the process several times and record her results in the table. What is the experimental probability of her selecting a red jelly bean?

• 11/33
• 1/3
• 1/4
• 18/26

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

Experimental Probability is:

• What Will happen 
• What actually happens
• What should happen
• What I think Happens

Here are the answers from the last slide

• 1,2,3,4,5,6

• P(1)=1/6

• P(even number)=1/2

• P(prime number)= 1/2

• P(2 or 3)= 2/6=1/3

Go to canvas and watch the first video

https://www.youtube.com/watch?v=BAjOEsU_mpE

Go to canvas and watch the 2nd video

https://www.youtube.com/watch?v=vbFWfmIyr3Q