Experimental & Theoretical Probability

by Hannah Ryan

| 22 QuestionsNote from the author:

Statistics

1

1

Which color do you think the spinner will land on in the image above?

Pink

Purple

Blue

Spin the wheel 10 times and record how many times the spinner lands on each color.

2

1

How many times did the spinner land on pink?

3

1

How many times did the spinner land on blue?

4

1

How many times did the spinner land on purple?

A Probability Scale is a numerical value from 0 to 1 that measures the likelihood of the event(s).

Drag the movable points below to display how likely it was for the spinner to land on each color.

5

1

Tim and Angela played 40 rounds with a one or more of the spinners above.

The table displays their results.

Which spinners did they most likely use?

(Select all)

A

B

C

D

Probability is a type of ratio where we compare how many times an outcome can occur compared to all possible outcomes.

The Probability of an Event can be written as a ratio, decimal, or percent.

6

1

When you flip a coin there are only two possible outcomes. (Heads or Tails)

Say you flip a coin 10 times, theoretically Heads will appear 5 times.

So the theoretical probability of flipping Heads is 1:2, ___ /___, or ______%.

[Separate your answers with commas & Simplify Fractions]

Theoretical Probability is what is expected to happen based on the possible outcomes, assuming equally likely events.

"What you expect to happen, but isn't always the case."

Flip the coin below 10 times and record the number of times you land on Heads.

7

1

How many times did you land on heads?

Experimental Probability is the result of an experiment or simulation after a large number of times.

"The probability determined from the results of an experiment."

8

1

What is the experimental probability fraction?

# Heads / Total # of Flips

[Simplify Fraction]

9

1

What is the experimental probability ratio?

# Heads : # Total Flips

[Simplify your answer]

Roll the die ten times and record the numbers in the table.

1st: Click "Reset" and count the number you see for Trial #1

2nd: press "Roll" to view Trials 2 - 10.

10

11

12

13

14

15

10

1

How many times did the #1 occur?

What is the Exp. Prob. Fraction?

11

1

How many times did the #2 occur?

What is the Exp. Prob. Fraction?

12

1

How many times did the #3 occur?

What is the Exp. Prob. Fraction?

13

1

How many times did the #4 occur?

What is the Exp. Prob. Fraction?

14

1

How many times did the #5 occur?

What is the Exp. Prob. Fraction?

15

1

How many times did the #6 occur?

What is the Exp. Prob. Fraction?

16

1

What do you think will happen to the Experimental Probability if you were to increase the number of times you rolled the die?

The experimental probability would move farther from the theoretical probability.

The experimental probability would reach closer to the theoretical probability.

17

1

Suppose you rolled the die 600 times.

Predict how many times you rolled a 3 or a 6.

Exactly 200 times.

Around 200 times.

18

1

Suppose you roll the die once.

What is the Theoretical Probability that you roll a number less than 3.

[Select all that apply]

2/6

3/6

1/3

1/2

≈ 33%

≈ 50%

Calculating Theoretical Probability when rolling two dice.

Use the table below to find the probability of rolling 2 dice that add to 7.

19

1

Use the table to list all of the combinations of numbers that sum to 7.

Ex: (a,b),(c,d),...

20

1

Find the probability:

P(rolling a sum of 7) = ?/36

[Write your answer in simplified fraction form]

In a sample of 55 students

3 have red hair.

16 have blonde hair.

12 have black hair.

24 have brown hair.

21

1

What is the probability a person has blonde or black hair?

[Write your answer in fraction form]

22

1

Find the probability that a person has neither brown nor black hair.

[Write your answer in fraction form]

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