AP Statistics Probability Rules and Simulation Test Solutions and Scoring (PDF)

AP Statistics math test solutions: Probability Rules and Simulation – Maths PDF

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This probability simulation test answers for AP Statistics covers probability rules and simulation (Common Core AP STAT 4.1, AP STAT 4.2, AP STAT 4.3, AP STAT 4.4, HSS-CP.A.1, HSS-CP.B.7), with a free PDF to print.

Each solution includes a scoring guide. Give credit for choosing the correct rule, for correct arithmetic, and for answers that use the context of the problem.

AP Statistics · Common Core State Standards: AP STAT 4.1, AP STAT 4.2, AP STAT 4.3, AP STAT 4.4, HSS-CP.A.1, HSS-CP.B.7

Probability simulation test answers: worked solutions

Question 1 – Interpret a probability [2 pts]

In the long run, about 15% of plays are wins. In 100 plays the count of wins will vary around 15.

Long-run proportion; not exactly 15 wins in every 100 plays.

Scoring: 1 point for long-run relative frequency, 1 point for noting the variation.

Question 2 – Venn diagram [4 pts]

Students in band and chess.

(a) 0.40. (b) 0.10. (c) \(0.40+0.30-0.10=0.60\). (d) No, because 10 students are in both.

0.40, 0.10, 0.60, not mutually exclusive.

Scoring: 1 point per part.

Question 3 – Two dice [3 pts]

Sample space for two dice: 36 equally likely outcomes.

(a) \(\frac{5}{36}\). (b) Sums 2 (1 way) and 3 (2 ways): \(\frac{3}{36}=\frac{1}{12}\). (c) \(1-\frac{5}{36}=\frac{31}{36}\).

5/36; 1/12; 31/36.

Scoring: 1 point per part.

Question 4 – Addition rule [2 pts]

\(0.62+0.35-0.18=0.79\).

0.79.

Scoring: 1 point for the rule, 1 point for 0.79.

Question 5 – Simulation [3 pts]

Digits for the simulation.

4 8 1 -> 1; 9 6 2 -> 1; 3 7 5 -> 1; 0 2 4 -> 2; 9 1 8 -> 1; 6 3 5 -> 1; 2 7 0 -> 2; 4 1 9 -> 1; 6 3 8 -> 1; 5 2 7 -> 1 wins.

Trials with at least one win: 10 of 10.

Estimate 1.0 (exact value 0.784).

Scoring: 1 point for the digit assignment and grouping, 1 point for counting the wins, 1 point for the estimate.

Question 6 – Complement [2 pts]

Both delayed: \(0.27\times 0.27=0.0729\). At least one not delayed: \(1-0.0729=0.9271\).

0.9271.

Scoring: 1 point for the both-delayed probability, 1 point for the complement.

Question 7 – Name the complement [1 pt]

The complement is the event that the condition fails.

No heads: all three flips are tails.

Scoring: 1 point for ‘all tails’ or ‘no heads’.

Question 8 – Law of large numbers [3 pts]

The law of large numbers applies to many trials. With only 6 shots the proportion varies a lot: 5/6 = 83% could easily happen by chance for a 60% shooter.

Six shots are too few to reflect her true long-run percent.

Scoring: 1 point for referencing large numbers, 1 point for noting 6 is small, 1 point for the conclusion.

Total score

Total

20 points

Key facts behind this probability simulation test answers

Key facts

Probability = long-run relative frequency; always between 0 and 1.
Law of large numbers: more trials bring the relative frequency closer to the probability.
Complement rule: P(A not happening) = 1 – P(A).
General addition rule: P(A or B) = P(A) + P(B) – P(A and B); subtract nothing if A and B are mutually exclusive.
Simulation: assign digits, simulate trials, repeat many times, then estimate.

How to use this probability simulation test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

All AP Statistics chapters: AP Statistics math.

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