Completed probability worksheet demonstrating how to calculate experimental probability from actual results and compare it with theoretical probability using card and survey examples.

Let’s go step by step through each question. We’ll use the data from Amanda’s card experiment and Dale’s eye color survey to find probabilities.

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Amanda’s Card Experiment (30 total draws)

She drew cards 30 times, replacing each time. The results:

- Diamonds: 7
- Hearts: 9
- Spades: 11
- Clubs: 3
→ Total = 7 + 9 + 11 + 3 = 30

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Question 1: Experimental probability of selecting a heart?

Experimental probability = (number of times heart was drawn) / (total draws)

= 9 / 30 → simplify: divide numerator and denominator by 3 → 3/10

✔ Answer: 3/10

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Question 2: Theoretical probability of selecting a heart?

In a standard deck, there are 52 cards, 13 hearts.

Theoretical probability = 13 / 52 → simplify: divide by 13 → 1/4

✔ Answer: 1/4

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Question 3: Experimental probability of diamond OR spade?

Diamonds: 7, Spades: 11 → total favorable = 7 + 11 = 18

Total draws = 30

Probability = 18 / 30 → simplify: divide by 6 → 3/5

(You can also add fractions: 7/30 + 11/30 = 18/30 = 3/5)

✔ Answer: 3/5

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Question 4: Theoretical probability of diamond OR spade?

In a deck: 13 diamonds + 13 spades = 26 cards

Total cards = 52

Probability = 26 / 52 = 1/2

(Or: 13/52 + 13/52 = 26/52 = 1/2)

✔ Answer: 1/2

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Question 5: Compare experimental and theoretical results.

Experimental for heart: 3/10 = 0.3
Theoretical for heart: 1/4 = 0.25 → difference is 0.05 (within 10%? Let’s check later)

Experimental for diamond/spade: 3/5 = 0.6
Theoretical: 1/2 = 0.5 → difference is 0.1 → which is exactly 10% of 0.5? Wait — let’s think carefully.

Actually, “within 10% of each other” usually means the *relative* difference is less than 10%.

But in this case, since it's a small sample (only 30 trials), we expect some variation.

The student wrote: “not the same but within 10% of each other.” That’s acceptable for school level.

We can say: They’re close, not exact — because experimental depends on chance in small samples, while theoretical is what should happen over many trials.

✔ Answer: They are not the same, but they are fairly close. This is normal with small experiments — as you do more trials, experimental gets closer to theoretical.

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Dale’s Eye Color Survey (80 students total)

Eye colors:

- Blue: 12
- Brown: 58
- Green: 2
- Hazel: 8
→ Total = 12 + 58 + 2 + 8 = 80

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Question 6a: Experimental probability distribution

P(blue) = 12/80 → simplify: divide by 4 → 3/20

P(brown) = 58/80 → divide by 2 → 29/40

P(green) = 2/80 → divide by 2 → 1/40

P(hazel) = 8/80 → divide by 8 → 1/10

✔ Answers:
- P(blue) = 3/20
- P(brown) = 29/40
- P(green) = 1/40
- P(hazel) = 1/10

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Question 6b: Probability student has blue OR green eyes?

Blue: 12, Green: 2 → total = 14

P = 14/80 → simplify: divide by 2 → 7/40

✔ Answer: 7/40

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Question 6c: Probability student does NOT have green or hazel eyes?

Green or hazel = 2 + 8 = 10 students

So NOT green or hazel = 80 - 10 = 70 students

P = 70/80 → simplify: divide by 10 → 7/8

Alternatively: 1 - P(green or hazel) = 1 - (10/80) = 1 - 1/8 = 7/8

✔ Answer: 7/8

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Question 6d: If grade has 360 students, how many expected to have brown eyes?

From survey, P(brown) = 58/80 = 29/40

Expected number = (29/40) × 360

Calculate:

First, 360 ÷ 40 = 9

Then 9 × 29 = ?

9 × 30 = 270 → minus 9 = 261

✔ Answer: 261 students

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Final Answer:
1. 3/10
2. 1/4
3. 3/5
4. 1/2
5. They are not the same, but fairly close — experimental varies due to small sample size; theoretical is long-term expectation.
6a. P(blue)=3/20, P(brown)=29/40, P(green)=1/40, P(hazel)=1/10
6b. 7/40
6c. 7/8
6d. 261 students