Empirical Probabilities

Probability: Theoretical vs. Experimental

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What is 'Probability'?

Probability is the measure of how likely it is for an event to occur.

Probability can be written as either a fraction, decimal or percentage.

Types of Probability

There are two types of Probability - Theoretical and Experimental.

Theoretical Probability measures what we would expect to happen based on all of the possible outcomes and those we would like to have happen.

Experimental Probability is the measurement based on data from trials of an experiment, and the number of favorable outcomes during that time.

Multiple Choice

• $$\frac{4}{36}$$

• $$\frac{9}{36}$$

• $$\frac{1}{4}$$

• $$\frac{1}{2}$$

Multiple Choice

Find  $$P\left(3\right)$$  when rolling a number a fair cube (or die). What is the Theoretical Probability?

• $$\frac{1}{6}$$

• $$\frac{3}{6}$$

• $$\frac{1}{2}$$  

• $$\frac{2}{3}$$  

Multiple Choice

What is  $$P\left(even\right)$$  when rolling a fair number cube? Find the Theoretical Probability

• $$\frac{1}{2}$$  

• $$\frac{1}{6}$$  

• $$\frac{1}{3}$$  

• $$\frac{2}{6}$$  

Multiple Choice

• 40%

• 20%

• 30%

• 50%

Multiple Choice

A class tossed coins and recorded 161 heads and 179 tails. What is the experimental probability of tossing a coin and the outcome being heads?

• $$\frac{161}{179}$$

• $$\frac{179}{161}$$

• $$\frac{161}{340}$$

• $$\frac{179}{340}$$

Multiple Choice

Another class rolled number cubes. The results are shown in the table. What is the experimental probability of rolling a 5?

• $$16.4\%$$

• $$19.7\%$$

• $$17.5\%$$

• $$16.8\%$$

Multiple Choice

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one marble from the jar at random. Find the theoretical probability P(red)

• $$0.3$$

• $$0.5$$

• $$0.4$$

• $$0.2$$

Multiple Choice

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one marble from the jar at random. Find the theoretical probability P(not white)

• $$0.3$$

• $$0.5$$  

• $$0.4$$  
  

• $$0.5$$

• $$0.7$$  

Multiple Choice

A jar contains 30 red marbles, 50 blue marbles, and 20 white marbles. You pick one marble from the jar at random. Find the theoretical probability P(red or blue)

• $$0.3$$

• $$0.5$$  

• $$0.4$$  
  

• $$0.5$$

• $$0.7$$  

Multiple Choice

A bag contains 36 red blocks, 48 green blocks, 22 yellow blocks, and 19 purple blocks. You pick one block from the bag at random. Find the theoretical probability P(not yellow)

• $$38.4$$

• $$82.4\%$$

• $$15.2\%$$

• $$61.6\%$$

• $$71.2\%$$

Multiple Choice

A bag contains 36 red blocks, 48 green blocks, 22 yellow blocks, and 19 purple blocks. You pick one block from the bag at random. Find the theoretical probability P(yellow or not green)

• $$38.4$$

• $$82.4\%$$

• $$15.2\%$$

• $$61.6\%$$

• $$71.2\%$$

Multiple Choice

What is the P( not purple) on this spinner?

• 2/5

• 1/5

• 4/5

• 3/5

Multiple Choice

What is the probability of spinning an even number?

• 16 2/3%

• 33 1/3%

• 50%

• 75%

Multiple Choice

You pick a marble from this bag.
What is the probability you will choose either a black or white marble?

• 3/5
• 9/100
• 1/10
• 2/5

Multiple Choice

A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?

• 3/10

• 3/9

• 1/9

• 9/1

Multiple Choice

What is the probability of rolling a cube and having it land as a six?

• 1/6
• 5/6
• 1/3
• 1/2

Multiple Choice

What is the probability of rolling a cube and having land as an odd number?

• 15%

• 33%

• 50%

• 75%

Multiple Choice

What is the probability of the spinner landing on an odd number?

• 50%

• 40%

• 30%

• 20%

Multiple Choice

Is it more likely or less likely to pull a red marble than a green marble?

• more likely

• less likely

• even probability

Multiple Choice

What is the probability of flipping a coin and getting heads?

• 1/2
• 1/3
• 1/4
• Never, Tails never fails.

Multiple Choice

A bag contains 5 quarters, 2 dimes, and 4 pennies. What is the probability of picking a quarter?

• 5/11
• 5/6
• 1/3
• 5

Multiple Choice

Experimental Probability is:

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

Multiple Choice

Theoretical Probability is?

• What Should happen
• What does happen
• What Will Happen
• What I want to Happen

Multiple Choice

The arrow is spun 15 times and landed 4 times on the section labeled Q. Which statement is true?

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 44 times and record her results in the table. What is the experimental probability of her selecting a red jelly bean?

Multiple Choice

A dice was rolled five times and the following were rolled: 1, 3, 3, 4, 4

Based on this information, find the experimental P(1).

• 3/5
• 1/6
• 2/5
• 1/5

Multiple Choice

Shannon has a bag of jelly beans.

5 Green

2 Red

3 Blue

What is the experimental probability of her selecting a red jelly bean?

• 11/33

• 2/10

• 1/5

• 23/30

Multiple Choice

What is the theoretical probability of the spinner landing on a section that is green or red ?

• 2/6

• 1/5

• 2/5

• 1/5

Multiple Choice

What is the experimental probability of the spinner landing on a section that is green or red ?

• 5/10

• 1/2

• 2/5

• 1/5

Multiple Select

What is the theoretical probability of flipping a coin and it lands on heads ? More than one answer can be correct

• 1/2

• 50%

• 3/8

• 37.5%

• 3.75%

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