7th Grade Compound Events and Simulations Worksheet Solutions (PDF)

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

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This compound events 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 to check your work on the compound events worksheet. Every solution shows the steps, and the final answer appears in bold. If your answer is different, compare each step and look for the first place where the work changes.

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

Compound events answers: exercises 1 to 10

Exercise 1 – Two coin tosses

First toss H or T, then second toss H or T.

HH, HT, TH, TT

Exercise 2 – Two heads

1 favorable outcome (HH) out of 4.

\(\frac{1}{4}\)

Only HH has two heads.

Exercise 3 – At least one head

Favorable outcomes: HH, HT, TH, which is 3 of 4.

\(\frac{3}{4}\)

Exercise 4 – Spinner and coin

Outcomes: 1H, 1T, 2H, 2T, 3H, 3T, which is \(3\times 2=6\).

P(2 and tails) = \(\frac{1}{6}\)

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

Exercise 5 – Sum of 7

The sum 7 occurs 6 times among 36 outcomes.

\(\frac{6}{36}=\frac{1}{6}\)

\(\frac{1}{6}\)

Exercise 6 – Large sums

Sum 11: (5, 6), (6, 5). Sum 12: (6, 6). That is 3 outcomes.

\(\frac{3}{36}=\frac{1}{12}\)

\(\frac{1}{12}\)

Exercise 7 – Doubles

Doubles: (1,1), (2,2), …, (6,6), which is 6 outcomes of 36.

\(\frac{6}{36}=\frac{1}{6}\)

\(\frac{1}{6}\)

Exercise 8 – Outfits

\(3\times 2=6\) outfits.

One favorable outcome: \(\frac{1}{6}\)

6 outfits; \(\frac{1}{6}\)

Exercise 9 – Tree diagram

Leaves: \(3\times 2=6\).

\(P(\text{blue, heads})=\frac{1}{6}\)

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

Exercise 10 – With replacement

\(P(\text{red})=\frac{2}{3}\) each time.

\(\frac{2}{3}\times\frac{2}{3}=\frac{4}{9}\)

\(\frac{4}{9}\)

Exercises 11 and up

Exercise 11 – Without replacement

First red: \(\frac{2}{3}\). Then 1 red of 2 marbles remains: \(\frac{1}{2}\).

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

\(\frac{1}{3}\)

The tree for two draws.

Exercise 12 – Three children

Outcomes: BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG (8 in all).

Exactly two girls: BGG, GBG, GGB, which is 3 outcomes.

\(\frac{3}{8}\)

\(\frac{3}{8}\)

Exercise 13 – Design a simulation

Let the digits 0, 1, 2, 3, 4, 5 mean a made shot (6 digits of 10 = 60%).

Let 6, 7, 8, 9 mean a miss.

Read two digits at a time; each pair is one trial of two shots.

Digits 0 to 5 = made; 6 to 9 = missed

Exercise 14 – Simulation results

Pairs with both digits 0 to 5: 14, 02, 51, 33, which is 4 of 10.

Experimental: \(\frac{4}{10}=0.4\), close to 0.36.

0.4 versus 0.36

Exercise 15 – Lunch combos

\(4\times 3\times 2=24\) meals.

One favorable meal: \(\frac{1}{24}\)

24 meals; \(\frac{1}{24}\)

Exercise 16 – Passwords

AA, AB, AC, BA, BB, BC, CA, CB, CC (9 passwords).

Same letters: AA, BB, CC, which is 3 of 9.

\(\frac{3}{9}=\frac{1}{3}\)

\(\frac{1}{3}\)

Exercise 17 – Carnival game

Total outcomes: \(4\times 4=16\).

Sum 6: (2,4), (3,3), (4,2). Sum 7: (3,4), (4,3). Sum 8: (4,4). That is 6 outcomes.

\(\frac{6}{16}=\frac{3}{8}\)

\(\frac{3}{8}\)

Counting favorable outcomes.

Exercise 18 – Even product

Both odd: \(3\times 3=9\) outcomes.

Even product: \(36-9=27\) outcomes.

\(\frac{27}{36}=\frac{3}{4}\)

\(\frac{3}{4}\)

Exercise 19 – Weather days

Toss a coin 3 times; heads means rain.

Outcomes with exactly two heads: HHT, HTH, THH.

HHT, HTH, THH (3 of 8)

Exercise 20 – Rock, paper, scissors

\(3\times 3=9\) outcomes.

Ties: RR, PP, SS, which is 3 of 9.

\(\frac{3}{9}=\frac{1}{3}\)

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

Key facts behind this compound events 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 answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

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