Sample spaces for compound events. Game on.

Sample spaces for compound events is a grade 7 math skill aligned to Common Core standard 7.SP.C.8.b. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 15 sample spaces for compound events problems our math games drill.

CCSS 7.SP.C.8.b15 questions in the bank
Kickoff

8 plays. No signup.

Warm-upeasy

A cafeteria offers 33 mains and 44 sides. How many outcomes are in the sample space of (main, side) meals?

A tree diagram starts with 33 branches for the mains. Each of those splits into 44 side branches, so the sample space has 3×4=12.3 \times 4 = 12\textsf{.}

Mid-gameeasy

Mia can pick from 55 shirts and 22 hats. How many outcomes are in the sample space of (shirt, hat) outfits?

A tree diagram starts with 55 branches for the shirts. Each of those splits into 22 hat branches, so the sample space has 5×2=10.5 \times 2 = 10\textsf{.}

Mid-gameeasy

A spinner with 33 equal sections is spun, and a standard six-sided die is rolled. How many outcomes are in the sample space?

A tree diagram starts with 33 branches for the spinner. Each of those splits into 66 die branches, so the sample space has 3×6=18.3 \times 6 = 18\textsf{.}

Mid-gameeasy

A juice stand offers 44 sizes and 55 flavors. How many outcomes are in the sample space of (size, flavor) drinks?

A tree diagram starts with 44 branches for the sizes. Each of those splits into 55 flavor branches, so the sample space has 4×5=20.4 \times 5 = 20\textsf{.}

Mid-gameeasy

Two fair coins are flipped. What is the probability of getting exactly one head?

The sample space is HH, HT, TH, and TT. Exactly one head appears in HT and TH, so 22 out of 44 equally likely outcomes, or 24=12.\dfrac{2}{4} = \dfrac{1}{2}\textsf{.}

Mid-gameeasy

A sandwich shop offers 66 breads and 44 fillings. How many outcomes are in the sample space of (bread, filling) sandwiches?

A tree diagram starts with 66 branches for the breads. Each of those splits into 44 filling branches, so the sample space has 6×4=24.6 \times 4 = 24\textsf{.}

Mid-gameeasy

Two standard six-sided dice are rolled. How many outcomes are in the sample space?

A tree diagram starts with 66 branches for the first die. Each of those splits into 66 branches for the second die, so the sample space has 6×6=36.6 \times 6 = 36\textsf{.}

Buzzer beatereasy

A spinner with 22 equal sections labeled yes and no is spun twice. What is the probability both spins land on yes?

The sample space is YY, YN, NY, and NN. Both spins are yes in only YY, so 11 out of 44 equally likely outcomes, or 14.\dfrac{1}{4}\textsf{.}

Overtime

7 more. Played, not assigned.

The rest of the bank lives inside live head-to-head matches — the placement test finds the right starting difficulty.

Batting Cage game coverBatting CagePlay →Blaster Gate game coverBlaster GatePlay →Blitz Tanks game coverBlitz TanksPlay →Buzzer Beater game coverBuzzer BeaterPlay →
Tests that cover sample spaces for compound events:
NAEPPSAT 8/9SBACSC READYNC EOG/EOC
Reporting domains for this skill
SAT All grades: Problem-Solving and Data AnalysisACT All grades: Preparing for Higher MathSTAAR Grade 7: Data Analysis, Personal Financial Literacy, and ProbabilityMAP Growth Math 6+: Statistics and Probabilityi-Ready Grade 7: Statistics and ProbabilitySBAC Grade 7: Concepts and Procedures
More Grade 7 skills
Simple interestVolume of prisms and cylindersProbability of simple eventsRatios, rates, and proportionsSampling and inferenceTable problems with percents and ratios (ACT)Triangle inequalityProbability from number setsAll Grade 7 practice →

Drill it inside a game.

The free placement test finds your level, then every match serves sample spaces for compound events questions at exactly the right difficulty.