Experimental Probability. 8th Grade Math Worksheets and Answers ... - Free Printable

Let’s go through each problem one by one. We’ll solve them step by step, using simple math and logic.

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Problem 1:

A six-sided die is rolled 50 times. The number 4 appears 18 times.

Experimental probability = (number of times event happened) ÷ (total number of trials)

So:
18 ÷ 50 = 0.36

✔ Answer: D. .36

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Problem 2:

Nathan spins a spinner 10 times. Results: B, B, C, E, F, B, D, A, E, C

We want the experimental probability he will spin a B.

Count how many times B appears:
First letter: B → 1
Second: B → 2
Sixth: B → 3
That’s it — 3 times.

Total spins = 10

Probability = 3 ÷ 10 = 0.3

But wait — look at the answer choices:
A. .17
B. .29
C. .3
D. .43

.3 is option C

✔ Answer: C. .3

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Problem 3:

Bag has:
- 3 green
- 4 pink
- 2 blue
Total marbles = 3 + 4 + 2 = 9

Rachel picks a marble, writes down result, puts it back → so each pick is independent, same total every time.

Her results: P, P, G, B, G, P, B, G, P, G, P, B, P, G, B → that’s 15 picks.

We need to count how many times she picked pink (P).

List:
1. P
2. P
3. G
4. B
5. G
6. P
7. B
8. G
9. P
10. G
11. P
12. B
13. P
14. G
15. B

Count the P’s: positions 1,2,6,9,11,13 → that’s 6 times

Total picks = 15

Probability = 6 ÷ 15 = 0.4

✔ Answer: A. .40

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Problem 4:

Coin flipped 20 times. Results: H, H, T, T, T, H, T, T, H, T, T, T, H, T, T, T, H, T, T, T

We want probability of getting a tail (T).

Count the T’s:

Let’s go one by one:

1. H
2. H
3. T → 1
4. T → 2
5. T → 3
6. H
7. T → 4
8. T → 5
9. H
10. T → 6
11. T → 7
12. T → 8
13. H
14. T → 9
15. T → 10
16. T → 11
17. H
18. T → 12
19. T → 13
20. T → 14

Wait — let me recount carefully.

Write the sequence again:

H, H, T, T, T, H, T, T, H, T, T, T, H, T, T, T, H, T, T, T

Group them:

Positions with T:
3,4,5 → 3
7,8 → 2 more → total 5
10,11,12 → 3 more → total 8
14,15,16 → 3 more → total 11
18,19,20 → 3 more → total 14

Yes, 14 tails.

Total flips = 20

Probability = 14 ÷ 20 = 0.7

✔ Answer: D. .70

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Problem 5:

25 students asked favorite number from 1–9.

Results:
- 8 said 3
- 6 said 4
- 9 said 7
- 2 said 8

Total = 8+6+9+2 = 25 ✔️

We want probability that a student picked 3.

Number who picked 3 = 8

Probability = 8 ÷ 25 = 0.32

✔ Answer: A. .24? Wait — 8/25 = 0.32 → that’s option C

Options:
A. .24
B. .32 ← this is correct
C. .34
D. .36

Wait — I think I misread. Let me check:

The question says: “What was the experimental probability that the number 3 was picked?”

Yes — 8 out of 25 → 8 ÷ 25 = 0.32

So answer is B. .32

✔ Answer: B. .32

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Problem 6:

Caleb picked 10 letters from alphabet. Results: H, J, X, A, N, O, I, N, B, C

We want probability he picked an N.

Count N’s:
Position 5: N
Position 8: N
→ 2 times

Total picks = 10

Probability = 2 ÷ 10 = 0.2

✔ Answer: D. .20

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Problem 7:

Spinner spun 75 times. Number seven appears 17 times.

Is the experimental probability of getting seven greater than theoretical?

First, what’s the theoretical probability?

Look at the spinner image — it shows numbers 1 through 8, equally sized sections → so 8 possible outcomes.

Theoretical probability of spinning a 7 = 1/8 = 0.125

Experimental probability = 17 ÷ 75 ≈ ?

Calculate: 17 ÷ 75 = 0.2266...

Which is about 0.227

Compare:
Theoretical = 0.125
Experimental = ~0.227 → which is GREATER

So statement: “The experimental probability... is greater than the theoretical” → TRUE

✔ Answer: A. true

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Problem 8:

Word: PARALLELOGRAM

Letters: P, A, R, A, L, L, E, L, O, G, R, A, M → let’s count total letters.

P-A-R-A-L-L-E-L-O-G-R-A-M → 13 letters

How many L’s?
Positions: 5,6,8 → three L’s

So theoretical probability of picking L = 3/13 ≈ 0.2308

Now, experiment: picked 50 times, L appeared 11 times.

Experimental probability = 11 ÷ 50 = 0.22

Compare:
Theoretical ≈ 0.2308
Experimental = 0.22 → which is LESS than theoretical

So: “The experimental probability is ___ the theoretical.”

Answer: less than

✔ Answer: B. less than

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Problem 9:

Die rolled, results: 2, 4, 6, 1, 5, 1, 6, 3, 2, 4, 5, 6, 1, 6

Count how many times 6 appears:

List:
1. 2
2. 4
3. 6 → 1
4. 1
5. 5
6. 1
7. 6 → 2
8. 3
9. 2
10. 4
11. 5
12. 6 → 3
13. 1
14. 6 → 4

So 6 appears 4 times.

Total rolls = 14

Experimental probability = 4 ÷ 14 ≈ 0.2857

Theoretical probability for rolling a 6 on a fair die = 1/6 ≈ 0.1667

Is 0.2857 close to 0.1667? Not really — it’s almost double.

But the question says: “is close to”

In some contexts, maybe — but let’s see the options.

It says: True or false?

Given that 4/14 = 2/7 ≈ 0.286 vs 1/6 ≈ 0.167 — difference is about 0.12, which is significant.

Probably not “close”.

But let’s check if they mean something else.

Wait — maybe I miscounted.

Results: 2,4,6,1,5,1,6,3,2,4,5,6,1,6 → yes, 14 numbers.

6s at positions 3,7,12,14 → 4 times.

4/14 = 2/7 ≈ 0.2857

1/6 ≈ 0.1667

Difference is large.

So likely FALSE.

But let’s see what the answer choices say.

A. true
B. false

I think it’s false — not close.

✔ Answer: B. false

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Problem 10:

Theoretical probability for spinner to land on blue is 1/4.

Spinner shown — looks like 4 equal sections: red, yellow, green, blue → yes, so 1/4 is correct.

Experiment: spun 150 times.

We want how many times it should land on blue to have experimental probability CLOSE to theoretical.

Theoretical = 1/4 = 0.25

So expected number = 0.25 × 150 = 37.5

Closest whole number is 38.

Options:
A. 24
B. 30
C. 38
D. 60

✔ Answer: C. 38

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## Final Answers:

1. D
2. C
3. A
4. D
5. B
6. D
7. A
8. B
9. B
10. C