Intro to Probability: Theoretical vs. Experimental

Probability: Theoretical vs. Experimental

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)

• $0.3$

•  $0.6$  

•  $0.8$  
  

•  $0.5$ 

•  $0.7$  

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)

• $0.3$

•  $0.6$  

•  $0.8$  
  

•  $0.5$ 

•  $0.7$  

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)

• $38.4\%$

• $82.4\%$

• $15.2\%$

• $61.6\%$

• $71.2\%$