← Back to the Statistical Experiments And Simulation worksheet
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: S-IC.A.2, S-IC.B.5, S-IC.B.6, S-MD.B.6, S-MD.B.7 · Level: Grade 11 Algebra 2
Problem 1 Assign random digits
Let the digits 0, 1, 2, 3, 4, 5 (six of ten) stand for an in-bounds serve and 6, 7, 8, 9 for a fault. Then an in-bounds serve has probability 6/10. Digits 0–5 = in bounds, 6–9 = fault.
Problem 2 Run a simulation by hand
Digits 0–6 are makes: 3, 1, 0, 6, 2, 4, 5 are makes (7 of them); 7, 8, 9 are misses. 7 makes in 10 shots.
Problem 3 Estimate a probability from trials
46 ÷ 200 = 0.23. ≈ 0.23.
Problem 4 Compare a simulation with theory
Experimental: 7/50 = 0.14. Theoretical: (1/2)(1/2)(1/2) = 1/8 = 0.125. 0.14 compared with 0.125: close, and the gap is the normal variation of a small simulation.
Problem 5 Is the coin fair? (14 heads)
The bars for 14, 15 and 16 heads show 4, 2 and 1 runs: 7 of 100 runs, or 7%. A result this extreme happens about 7% of the time with a fair coin, which is not rare. 7 runs; a fair coin is plausible.
Problem 6 Is the coin fair? (18 heads)
No bar extends past 16 heads, so 0 of the 100 runs had 18 or more. 0 runs; 18 heads is very unlikely with a fair coin, so the coin is probably biased.
Problem 7 Parts of an experiment
Treatments: energy drink and plain water (the water group is the control). Response variable: reaction time. Random assignment makes the two groups alike in other ways, so a difference can be credited to the drink. Treatments: drink or water; response: reaction time; random assignment balances other factors.
Problem 8 Correlation and causation
No. Students chose whether to eat breakfast, so this is an observational study. Other factors, such as sleep or family routine, may affect both breakfast and GPA. No: only a randomized experiment can support cause and effect.
Problem 9 Evaluate a poll
The respondents chose themselves, so fans of the restaurant are over-represented (voluntary response bias). The question is also leading. Self-selected sample and a leading question.
Problem 10 Sample size and margin of error
For 100: 1/10 = 0.10. For 1000: 1/√1000 = 0.0316. ≈ 0.10 (10 points) and ≈ 0.032 (3.2 points): ten times the sample size cuts the margin by about a factor of 3.
Problem 11 Re-randomization for two fertilizers
The bars for 4 and 5 cm show 3 + 1 = 4 runs out of 100. A difference this large occurred by chance only 4% of the time. 4 of 100 runs (4%).
Problem 12 Draw a conclusion from the simulation
Since 4% is below 5%, a difference of 4 cm would be unusual by chance alone. Yes: there is evidence that fertilizer A produces more growth than fertilizer B, and because the plants were randomly assigned, the fertilizer can be credited.
Problem 13 Choose fairly among three options
Assign 1 and 2 to Ana, 3 and 4 to Ben, and 5 and 6 to Cara. Roll once. Each friend has 2/6 = 1/3 chance. Each has probability 1/3.
Problem 14 Is the game fair?
Expected winnings = 9(1/6) + 0(5/6) = $1.50. Net = 1.50 − 2 = −$0.50. Expected net −$0.50 per play, so the game is not fair.
Problem 15 Raffle expected value
Total prizes = 200 + 2(50) + 5(20) = 400, so the expected prize per ticket is 400/500 = $0.80. Net = 0.80 − 5 = −$4.20. Expected prize $0.80; expected net −$4.20.
Problem 16 Test a manufacturer’s claim
In the simulation, 15 or fewer long-lasting bulbs occurred 3 + 1 = 4 times in 100, or 4%. That is unusual if the claim were true. The claim is doubtful (a result this low happens about 4% of the time).
Problem 17 Warranty decision
Expected repair cost = 0.08(450) = $36. The warranty costs $60, which is $24 more than the expected cost. On average the warranty loses $24, so skipping it is better in expectation (though it removes the risk of a large bill).
Problem 18 Evaluate a tutoring report
Possible questions: (1) Were students assigned at random, or did they choose to enroll? (2) Was there a comparison group that did not receive tutoring? (3) Is a sample of 12 large enough to separate the 5-point rise from chance? Self-selection, no control group and a small sample all limit the conclusion.
Problem 19 Sure thing versus gamble
Plan A: $550. Plan B: 1000(0.6) + 0(0.4) = $600. Plan B has the higher expected value ($600 versus $550), but it carries the risk of $0.
Problem 20 Compare two machines
Machine X: 0.92(3) − 0.08(5) = 2.76 − 0.40 = $2.36. Machine Y: 0.97(2.50) − 0.03(4) = 2.425 − 0.12 = $2.305. Machine X, with $2.36 versus about $2.31 per item.