7th Grade Compound Events and Simulations Test Solutions and Scoring (PDF)

7th Grade math test solutions: Compound Events and Simulations – Maths PDF

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This compound events test answers for 7th Grade covers compound events and simulations (Common Core 7.SP.C.8), with a free PDF to print.

Use this answer key and scoring guide to grade the compound events test. Each solution shows the full work, and the scoring note explains how the points are awarded. Give partial credit for correct steps even when the final answer is wrong.

Grade 7 · Common Core State Standards: 7.SP.C.8

Compound events test answers: worked solutions

Question 1 – Sample space [2 pts]

A1, A2, A3, B1, B2, B3.

A with an odd number: A1, A3, which is 2 of 6.

\(\frac{2}{6}=\frac{1}{3}\)

6 outcomes; \(\frac{1}{3}\)

Scoring: 1 point for the sample space; 1 point for the probability.

Question 2 – Two dice [2 pts]

Sum 8 occurs 5 times: \(\frac{5}{36}\).

Sums less than 4: 2 (once) and 3 (twice) = 3 outcomes: \(\frac{3}{36}=\frac{1}{12}\)

\(\frac{5}{36}\); \(\frac{1}{12}\)

Scoring: 1 point for each probability.

Question 3 – Counting principle [2 pts]

\(3\times 4\times 5=60\).

\(\frac{1}{60}\)

60 pizzas; \(\frac{1}{60}\)

Scoring: 1 point for the count; 1 point for the probability.

Question 4 – With replacement [2 pts]

\(\frac{3}{5}\times\frac{3}{5}=\frac{9}{25}\)

\(\frac{9}{25}\)

Scoring: 1 point for each probability used; the product earns the second point.

Question 5 – At least one [2 pts]

All outcomes: 8. No heads: TTT only, so \(\frac{1}{8}\).

\(1-\frac{1}{8}=\frac{7}{8}\)

\(\frac{7}{8}\)

Scoring: 1 point for P(no heads); 1 point for the complement.

Question 6 – Design a simulation [2 pts]

Let 0, 1, 2 mean blue and 3 to 9 mean not blue (3 of 10 = 30%).

Read three digits per trial; count trials with at least one of 0, 1, 2; divide by the number of trials.

Digits 0 to 2 = blue

Scoring: 1 point for the digit assignment; 1 point for the counting plan.

Question 7 – Simulation results [2 pts]

Check each trial for a digit 0, 1, or 2.

Hits: 912, 057, 616, 249, 130, 552, 408, 792. The trials 384 and 877 have none.

That is 8 of 10, so the estimate is 0.8.

0.8

Scoring: 1 point for identifying hits; 1 point for the estimate.

Question 8 – Spinner and coin [3 pts]

\(4\times 2=8\) outcomes.
2H and 4H: \(\frac{2}{8}=\frac{1}{4}\).
3T and 4T: \(\frac{2}{8}=\frac{1}{4}\).

Counts.

Scoring: 1 point for each part.

Question 9 – Dice differences [3 pts]

\(6\times 6=36\).
Pairs: (1,2), (2,3), (3,4), (4,5), (5,6) and the reverses, 10 in all: \(\frac{10}{36}=\frac{5}{18}\).
\(\frac{6}{36}=\frac{1}{6}\).

Counts.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this compound events test answers

Key facts

A compound event has two or more stages, such as two coin tosses.
The sample space lists every possible outcome.
Counting principle: \(m \times n\) outcomes for two stages with m and n ways.
Equally likely outcomes: \(P = favorable \div total\).
A simulation uses random numbers to estimate a probability.

How to use this compound events 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.

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