Experimental vs Theoretical Review with Tree Diagrms

Review and Something New

Objectives:

Review Experimental vs. Theoretical Probability ​

Introduce Tree Diagrams and the Counting Principle

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

Theoretical vs Experimental Probability

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

Experimental Probability

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

Tree Diagrams- Probability

By Ashley Carson

Tree Diagram

A tree diagram is a branching structure that maps the outcomes of chances/probabilities. The more branches, the more outcomes.

Tree Diagram

Flipping a coin. Your only outcomes are either head or tail. Your tree diagram would look like this:

Tree Diagram

Flipping a coin twice. If you flipped your coin a second time, you still only have the outcomes heads and tails but this time they branched out from your previous outcome. So your tree diagram would look like this:

Multiple Choice

What is the probability of getting 2 tails?

• 1/4

• 2/4

• 3/4

• 4/4

Tree Diagram

• Can be used to show a sample space

• Each "branch" of the diagram represents one possible outcome

Multiple Choice

What is the probability of making both shots?

• 1/4

• 2/4

• 3/4

• 4/4

Multiple Choice

How many possible outcomes or combinations can we get if we toss a coin, and roll a number cube?

• 6 total outcomes

• 8 total outcomes

• 14 total outcomes

• 12 total outcomes

Multiple Choice

Two dice are rolled and it is recorded whether the result on each is odd or even. What is the probability both are odd?

• 1/4

• 1/2

• 2/4

• 3/4

Multiple Choice

The probability of getting Broccoli and fish for dinner is:

• 0.5

• 0.15

• 0.7

• 1

The Counting Principle

• easier way to find a sample space

• helpful for a large number of outcomes

• multiply the number of possible outcomes for EACH "event"

• OR if looking for something specifically given, multiple both fractional probabilities together.

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag. What is the probability I select a red marble?

• $$\frac{1}{3}$$  

• $$\frac{2}{3}$$

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag. What is the probability I select a blue marble?

• $$\frac{1}{3}$$  

• $$\frac{2}{3}$$

Poll

Suppose a bag contains 2 red and 4 blue marbles. I select a marble from the bag, look at it, then replace it. Then I select a second marble from the bag. What is the probability I select a red marble then a blue marble?

• $$\frac{2}{9}$$

• $$\frac{2}{36}$$

• $$\frac{1}{18}$$

Alphabet Cards

• I have a stack of 52 alphabet cards

• 26 uppercase cards (A, B C, . . .)

• 26 lowercase cards (a, b, c, . . .)

• What is the probability I select one card and it is an uppercase vowel?

Fill in the Blank

I have a stack of 52 alphabet cards. 

26 uppercase cards (A, B C, . . .) 

26 lowercase cards (a, b, c, . . .) 

What is the probability I select one card and it is an uppercase vowel?

Chipotle

• Chipotle offers a variety of choices for food. How many options are there?

• You can have a burrito, bowl, salad or tacos

• Choices for protein include carne asada, chicken, steak, barbacoa, carnitas, sofritas or veggies

Chipotle

• Choices for rice include white, brown, cauliflower or no rice

• Choices for beans include black, pinto or no beans

• Choices for salsa include fresh tomato, corn, green tomatillo, red tomatillo or no salsa

• You can also have sour cream, fajita veggies, cheese or lettuce (or not!)

Don't forget the guac!

Chipotle

• Choices for rice include white, brown, cauliflower or no rice

• Choices for beans include black, pinto or no beans

• Choices for salsa include fresh tomato, corn, green tomatillo, red tomatillo or no salsa

• You can also have sour cream, fajita veggies, cheese or lettuce (or not!)

Fill in the Blank

How many possible menu items are there at Chipotle?

You have 4 different pairs of socks and 6 different pairs of sneakers. How many different combinations of socks and shoes do you have?

• 4 socks

• 6 sneakers

• 4x6=24 combinations

Fill in the Blank

At Joey's Italian Restaurant, there are 6 choices for appetizers and 8 choices for entrees. How many different appetizer and entree choices are there?

Multiple Choice

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

• 15

• 40

• 80

• 10

Multiple Choice

At  a New Car Dealership a particular model comes in 4 trim levels, 5 different colors, and 3 different interiors. How many different versions of this car model can be created from these options?

• 180

• 23

• 12

• 60