Probability Worksheet 4 - Experimental vs. Theoretical - Ellie ... - Free Printable

Let’s solve each question step by step.

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First, let’s count the tally marks for Amanda’s card experiment:

- Diamonds: |||| | → that’s 5 + 2 = 7
- Hearts: |||| |||| → that’s 5 + 4 = 9
- Spades: |||| |||| | → that’s 5 + 5 + 1 = 11
- Clubs: ||| → that’s 3

Total trials = 7 + 9 + 11 + 3 = 30

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Question 1: Experimental probability of selecting a heart?

Experimental probability = (number of times heart was picked) / (total trials)

= 9 / 30

Simplify: divide numerator and denominator by 3 → 3/10

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Question 2: Theoretical probability of selecting a heart?

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

So theoretical probability = 13 / 52 = 1/4

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Question 3: Experimental probability of selecting a diamond or a spade?

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

Probability = 18 / 30 = simplify by dividing by 6 → 3/5

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Question 4: Theoretical probability of selecting a diamond or a spade?

Diamonds = 13, Spades = 13 → total = 26

Probability = 26 / 52 = 1/2

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Question 5: Compare results and describe findings.

Experimental probabilities:
- Heart: 3/10 = 0.3
- Diamond or Spade: 3/5 = 0.6

Theoretical probabilities:
- Heart: 1/4 = 0.25
- Diamond or Spade: 1/2 = 0.5

→ The experimental results are close to theoretical but not exact. That’s normal — with more trials, they’d get closer. Also, in this case, hearts came up slightly more often than expected, and diamonds/spades also came up more often than expected. Clubs were underrepresented (only 3 times vs expected ~7.5).

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Now, Dale’s eye color survey:

Blue: 12
Brown: 58
Green: 2
Hazel: 8

Total students surveyed = 12 + 58 + 2 + 8 = 80

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Question 6a: Experimental probability distribution

P(blue) = 12 / 80 = 3/20
P(brown) = 58 / 80 = 29/40
P(green) = 2 / 80 = 1/40
P(hazel) = 8 / 80 = 1/10

*(You can leave as fractions simplified, or decimals if asked — but fractions are fine here.)*

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

Blue + Green = 12 + 2 = 14

Probability = 14 / 80 = 7/40

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

That means they have blue OR brown.

Blue + Brown = 12 + 58 = 70

Probability = 70 / 80 = 7/8

*(Alternatively: 1 - P(green or hazel) = 1 - (2+8)/80 = 1 - 10/80 = 70/80 = 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

Expected number = (58/80) × 360

Let’s calculate:

First, simplify 58/80 = 29/40

Then: (29/40) × 360 = 29 × (360 ÷ 40) = 29 × 9 = 261

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Final Answer:

1. 3/10
2. 1/4
3. 3/5
4. 1/2
5. Experimental results are close to theoretical; small differences are due to chance in limited trials. Hearts and diamond/spade occurred slightly more often than expected; clubs less often.
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