Math worksheet designed to teach students the difference between theoretical and experimental probability using colorful spinners and data recording.

Let’s solve this step by step.

We are given two spinners and their experimental results from 100 spins each. We need to fill in the table with theoretical probability (what should happen based on how many sections there are) and experimental probability (what actually happened, based on the frequency data).

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First, let’s understand what we’re calculating:

- Theoretical Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
- For Spinner #1: It has 4 equal sections → Blue, Green, Blue, Green → So 2 blue, 2 green → total 4 sections.
- For Spinner #2: It has 5 sections → Blue (2), Yellow (1), Red (1), Purple (1) → total 5 sections.

- Experimental Probability = (Frequency of event) / (Total trials = 100)

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## Let’s go row by row.

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Event 1: Spinner #1: Landing on blue

- Theoretical: There are 2 blue sections out of 4 → 2/4 = 1/2
- Experimental: From table, Blue came up 53 times → 53/100

→ Fill in:
Theoretical: 1/2
Experimental: 53/100

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Event 2: Spinner #2: Landing on green

Wait — look at Spinner #2 colors: Blue, Yellow, Red, Purple. There is no green!

So theoretical probability = 0/5 = 0

Experimental: Did it land on green? Looking at frequency table for Spinner #2: no “green” listed → so frequency = 0 → 0/100 = 0

→ Fill in:
Theoretical: 0
Experimental: 0

*(Note: This might be a trick question or typo — but based on the image, Spinner #2 has no green section.)*

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Event 3: Spinner #2: Landing on blue

- Theoretical: 2 blue sections out of 5 → 2/5
- Experimental: Blue came up 20 times → 20/100 = 1/5

→ Fill in:
Theoretical: 2/5
Experimental: 1/5

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Event 4: Spinner #2: Landing on either green or purple

Again — no green in Spinner #2. Only purple is present.

Purple appears once → so favorable outcomes: only purple → 1 out of 5 → 1/5

Experimental: Purple came up 9 times → 9/100

But wait — the event says “either green or purple”. Since green never happens, it’s just purple.

→ Theoretical: 1/5
Experimental: 9/100

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Event 5: Spinner #1: Landing on yellow

Spinner #1 has only Blue and Green → no yellow!

Theoretical: 0/4 = 0

Experimental: No yellow in frequency table → 0/100 = 0

→ Fill in:
Theoretical: 0
Experimental: 0

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Event 6: Spinner #2: Not landing on green

Since there is no green, “not landing on green” means landing on ANY color → which always happens.

Theoretical: All 5 sections are not green → 5/5 = 1

Experimental: Total spins = 100, none were green → so all 100 are “not green” → 100/100 = 1

→ Fill in:
Theoretical: 1
Experimental: 1

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Now, answer the questions below the table.

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Question 1: If you spin Spinner #1 400 times, about how many times would you expect it to land on blue?

Theoretical probability of blue on Spinner #1 = 1/2

Expected number = 400 × (1/2) = 200

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Question 2: If you spin Spinner #2 800 times, about how many times would you expect it to land on red?

Theoretical probability of red on Spinner #2 = 1/5

Expected number = 800 × (1/5) = 160

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Question 3: Three guys spun Spinner #1 100 times each and landed on green 48, 52, and 47 times. Which spinner did they use? Explain your answer.

They got around 48–52 greens out of 100 → that’s about half.

Spinner #1 has 2 green sections out of 4 → theoretical probability = 2/4 = 1/2 → so expecting ~50 greens in 100 spins → matches.

Spinner #2 has NO green → so if they used Spinner #2, they’d get 0 greens.

Therefore, they must have used Spinner #1.

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Final Answer:

Event 1: Theoretical = 1/2, Experimental = 53/100
Event 2: Theoretical = 0, Experimental = 0
Event 3: Theoretical = 2/5, Experimental = 1/5
Event 4: Theoretical = 1/5, Experimental = 9/100
Event 5: Theoretical = 0, Experimental = 0
Event 6: Theoretical = 1, Experimental = 1

Question 1: 200
Question 2: 160
Question 3: They used Spinner #1 because its theoretical probability of landing on green is 1/2, matching their results (~50 out of 100). Spinner #2 has no green, so it couldn’t produce those results.