7th Grade Math

7th Grade Math Quiz: Represent Sample Spaces For Compound Events

Practice Represent Sample Spaces For Compound Events in 7th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

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This quiz focuses on Represent Sample Spaces For Compound Events, giving you a quick way to practice the rules, question types, and explanations that matter most for 7th Grade Math.

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Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

Coach Rivera organizes team selections by having students draw one ball from Box 1 (containing balls labeled X, Y, Z) and one ball from Box 2 (containing balls labeled 1, 2, 3, 4). Students are assigned to the advanced team if they draw a ball from the second half of the alphabet (Y or Z) from Box 1 AND an even number from Box 2. Using a systematic table to represent this sample space, what portion of all possible outcomes results in advanced team assignment?

3 favorable outcomes out of 10 total possible drawing combinations
6 favorable outcomes out of 12 total possible drawing combinations
4 favorable outcomes out of 14 total possible drawing combinations
4 favorable outcomes out of 12 total possible drawing combinations

Explanation: When you encounter probability questions involving two separate events, you need to systematically list all possible combinations to find the sample space and identify favorable outcomes. Let's create a table showing all possible combinations. Box 1 has letters {X, Y, Z} and Box 2 has numbers {1, 2, 3, 4}:

Box 1	Box 2	Outcome
X	1	(X,1)
X	2	(X,2)
X	3	(X,3)
X	4	(X,4)
Y	1	(Y,1)
Y	2	(Y,2)
Y	3	(Y,3)
Y	4	(Y,4)
Z	1	(Z,1)
Z	2	(Z,2)
Z	3	(Z,3)
Z	4	(Z,4)

This gives us 12 total possible outcomes (3 letters × 4 numbers = 12). For advanced team assignment, students need: (1) second half of alphabet letter (Y or Z) AND (2) even number (2 or 4). The favorable outcomes are: (Y,2), (Y,4), (Z,2), (Z,4) — that's 4 favorable outcomes. Choice A incorrectly counts 10 total outcomes, missing some combinations. Choice B correctly identifies 12 total outcomes but miscounts 6 favorable outcomes, likely including all Y and Z combinations regardless of the number requirement. Choice C suggests 14 total outcomes, which is mathematically impossible with only 3 letters and 4 numbers. Remember: when dealing with compound probability events, always create a systematic table or tree diagram to avoid missing combinations or miscounting requirements.

Question 2

Tyler is analyzing outcomes for a game where he flips two coins and spins a wheel divided into 4 equal sections (numbered 1, 2, 3, 4). He needs to represent the sample space and identify outcomes where he gets exactly one head and a number less than 3 on the wheel. Which statement correctly describes this compound event?

The sample space contains 16 outcomes, and exactly 4 outcomes satisfy the given conditions
The sample space contains 12 outcomes, and exactly 3 outcomes satisfy the given conditions
The sample space contains 16 outcomes, and exactly 6 outcomes satisfy the given conditions
The sample space contains 8 outcomes, and exactly 2 outcomes satisfy the given conditions

Explanation: Sample space = 2 × 2 × 4 = 16 outcomes (each coin has 2 outcomes, wheel has 4). For exactly one head: either HT or TH with any wheel number. Numbers less than 3 are 1 and 2. Favorable outcomes: (H,T,1), (H,T,2), (T,H,1), (T,H,2) = 4 outcomes. Choice B undercounts the sample space. Choice C overcounts favorable outcomes. Choice D undercounts both.

Question 3

A board game uses two spinners: Spinner A with 3 equal sections (Win, Lose, Draw) and Spinner B with 2 equal sections (Bonus, No Bonus). Players spin both spinners simultaneously. If a tree diagram is used to represent all possible outcomes, and we want to identify the event 'player gets Win or Draw on Spinner A AND gets Bonus on Spinner B', how should this compound event be represented?

4 branches out of 6 total endpoints represent this event in the complete tree diagram
2 branches out of 6 total endpoints represent this event in the complete tree diagram
3 branches out of 5 total endpoints represent this event in the complete tree diagram
2 branches out of 5 total endpoints represent this event in the complete tree diagram

Explanation: The tree diagram has 3 × 2 = 6 total endpoints. The event requires (Win AND Bonus) OR (Draw AND Bonus), which gives exactly 2 favorable outcomes out of 6 total. Choice A incorrectly counts 4 outcomes (possibly including 'No Bonus' cases). Choices C and D incorrectly state 5 total endpoints when there should be 6.

Question 4

In a probability experiment, Jade rolls a standard die and draws a card from a deck containing 5 cards labeled A, B, C, D, E. She wants to identify all outcomes where the die shows a multiple of 3 AND the card is a vowel (A or E). If she represents the sample space using an organized list of ordered pairs, which analysis of this compound event is accurate?

The sample space has 30 outcomes, with exactly 4 outcomes satisfying both conditions simultaneously
The sample space has 25 outcomes, with exactly 4 outcomes satisfying both conditions simultaneously
The sample space has 30 outcomes, with exactly 6 outcomes satisfying both conditions simultaneously
The sample space has 11 outcomes, with exactly 2 outcomes satisfying both conditions simultaneously

Explanation: Sample space = 6 die outcomes × 5 card outcomes = 30 total outcomes. Die multiples of 3 are 3 and 6. Vowel cards are A and E. Favorable outcomes: (3,A), (3,E), (6,A), (6,E) = exactly 4 outcomes. Choice B undercounts the sample space. Choice C overcounts favorable outcomes. Choice D severely undercounts the sample space.

Question 5

Sarah creates an organized list to represent all possible outcomes when she draws one card from each of two decks: Deck A contains cards numbered 1, 3, 5 and Deck B contains cards numbered 2, 4, 6, 8. She wants to identify outcomes where the sum of the two cards is greater than 8. Which organized approach correctly represents this compound event?

A table with 4 rows and 4 columns showing 12 total outcomes, with 6 outcomes having sums greater than 8
A table with 3 rows and 4 columns showing 12 total outcomes, with 7 outcomes having sums greater than 8
A list of 12 ordered pairs with 7 pairs having sums greater than 8
A list of 8 ordered pairs with 4 pairs having sums greater than 8

Explanation: Since Deck A has 3 cards and Deck B has 4 cards, there are 3 × 4 = 12 total outcomes. The pairs with sums greater than 8 are: (1,8)=9, (3,6)=9, (3,8)=11, (5,4)=9, (5,6)=11, (5,8)=13, and (1,8)=9. Wait, that should be: (1,8)=9, (3,6)=9, (3,8)=11, (5,4)=9, (5,6)=11, (5,8)=13, and (1,8) was already counted. The correct 7 outcomes are: (1,8)=9, (3,6)=9, (3,8)=11, (5,4)=9, (5,6)=11, (5,8)=13, plus (5,2) is only 7, so actually: (1,8), (3,6), (3,8), (5,4), (5,6), (5,8) gives us 6... Let me recalculate: All sums > 8: (1,8)=9, (3,6)=9, (3,8)=11, (5,4)=9, (5,6)=11, (5,8)=13. That's only 6, not 7. Choice A incorrectly suggests a 4×4 table. Choice B correctly identifies the table dimensions but overcounts favorable outcomes. Choice D undercounts both total outcomes and favorable outcomes.

Question 6

A student flips a coin twice. Which set is the complete sample space for this compound event?

{H, T}
{HH, HT, TT}
{HH, HT, TH, TT}
{HH, TT}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coin flips {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches for each possibility, like four paths for two flips. For example, for a coin flip and die roll, the list is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two flips shows branches leading to HH, HT, TH, TT. The correct representation here is choice A, which lists all four possible outcomes for two coin flips. Common errors include omitting TH as in B, listing single flips as in C, or only matching outcomes as in D. When creating a list, systematically combine all outcomes from each flip, such as 2 times 2 equals 4. For identifying events, translate descriptions to locate and count, avoiding incomplete lists or confusing with single events.

Question 7

A student spins a spinner with 4 equal sections labeled A, B, C, D and then flips a coin. How many outcomes are in the complete sample space?

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coins {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping a coin twice yielding 4 paths. For example, a coin flip followed by a die roll has a list {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two coin flips shows paths HH, HT, TH, TT. The correct count here is choice B, 8 outcomes from 4 spinner results times 2 coin flips. Common errors include undercounting like 6 in A or overcounting like 12 in D, perhaps confusing spinner sections. When creating a sample space, multiply independent possibilities: 4 x 2 = 8. To identify the total, list systematically like A-H, A-T, etc.; mistakes often involve wrong multiplication or ignoring one event.

Question 8

A student flips a coin twice. Using the sample space {HH, HT, TH, TT}, which outcomes match the event “at least one head”?

{HH, HT, TH}
{HT, TH}
{TT}
{HH}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coin flips {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches for each possibility, like four paths for two flips. For example, for a coin flip and die roll, the list is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two flips shows branches leading to HH, HT, TH, TT. The correct representation here is choice D, which includes all outcomes with at least one head: HH, HT, TH. Common errors include only both heads as in A, only mixed as in B, or no heads as in C. When creating a list, systematically combine outcomes, then filter for the event like 'at least one'. For identifying events, translate phrases like 'at least' to include all matching, avoiding errors like excluding TH or miscounting.

Question 9

A student draws one colored tile from a bag, does not put it back, and then draws a second tile. The bag contains 2 red tiles (R) and 1 blue tile (B). If outcomes are written in order (first draw, second draw), which list is the complete sample space?

{RR, RB}
{RR, RB, BR}
{R, B}
{RR, RB, BR, BB}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coin flips {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches for each possibility, like four paths for two flips. For example, for a coin flip and die roll, the list is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two flips shows branches leading to HH, HT, TH, TT. The correct representation here is choice B, listing all possible outcomes without replacement: RR, RB, BR, excluding impossible BB. Common errors include including BB as in A, single draws as in C, or incomplete like D. When creating a list for without replacement, account for changing possibilities, like after drawing R, options are R or B. For identifying events, consider dependencies and avoid listing impossibles or confusing with replacement.

Question 10

Two different number cubes labeled 1–6 are rolled. Event $F$ is: “Both numbers are odd.” How many outcomes are in $F$ ?

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coins {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping a coin twice yielding 4 paths. For example, a coin flip followed by a die roll has a list {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two coin flips shows paths HH, HT, TH, TT. The correct count here is choice C, 9 outcomes where both are odd (3 odds per die: 3x3=9). Common errors include counting only one die's odds in A or overcounting in D. When creating a table, mark cells where both a and b are odd and count them. To identify and count, translate 'both odd' to qualifying pairs; mistakes often involve confusing 'both' with 'at least one' or wrong odd numbers.

Question 11

A student flips a coin and then rolls a number cube labeled 1–6. Which list shows the complete sample space for this compound event (coin result first, then number)?

{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T, HT, TH}
{H, T, 1, 2, 3, 4, 5, 6}
{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coins {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping a coin twice yielding 4 paths. For example, a coin flip followed by a die roll has a list {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two coin flips shows paths HH, HT, TH, TT. The correct representation here is choice B, which lists all 12 outcomes completely and accurately. Common errors include incomplete lists like missing T6 in choice A, ignoring combinations in choice C, or adding irrelevant outcomes like HT and TH in choice D. When creating a list, systematically combine all possibilities from each event, such as 2 coin outcomes times 6 die outcomes for 12 total. To identify the complete sample space, translate the sequence of events into ordered pairs and ensure all are enumerated without duplicates or omissions; mistakes often involve forgetting outcomes or confusing independent events.

Question 12

A student rolls two standard number cubes. Outcomes are ordered pairs (first roll, second roll). How many outcomes are in the event “the sum is 8”?

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coin flips {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches for each possibility, like four paths for two flips. For example, for a coin flip and die roll, the list is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two flips shows branches leading to HH, HT, TH, TT. The correct representation here is choice B, with 5 outcomes where the sum is 8: (2,6), (3,5), (4,4), (5,3), (6,2). Common errors include undercounting to 4 or 6, or listing total outcomes as 36. When creating a table, fill a 6x6 grid and count cells meeting the condition. For identifying events, translate 'sum is 8' and count carefully, avoiding mistakes like ignoring (4,4) or double-counting.

Question 13

Two different number cubes labeled 1–6 are rolled. Event $F$ is: “Both numbers are odd.” How many outcomes are in $F$ ?

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coins {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping a coin twice yielding 4 paths. For example, a coin flip followed by a die roll has a list {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two coin flips shows paths HH, HT, TH, TT. The correct count here is choice C, 9 outcomes where both are odd (3 odds per die: 3x3=9). Common errors include counting only one die's odds in A or overcounting in D. When creating a table, mark cells where both a and b are odd and count them. To identify and count, translate 'both odd' to qualifying pairs; mistakes often involve confusing 'both' with 'at least one' or wrong odd numbers.

Question 14

A student flips a coin, then flips the coin again. Which set correctly represents the complete sample space?

{HT, TH, TT}
{HH, HT, TT}
{HH, HT, TH, TT}
{H, T}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coins {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping a coin twice yielding 4 paths. For example, a coin flip followed by a die roll has a list {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two coin flips shows paths HH, HT, TH, TT. The correct representation here is choice B, the complete set {HH, HT, TH, TT}. Common errors include missing TH in A, single flips in C, or excluding HH in D. When creating a list, enumerate all ordered pairs from two independent flips. To identify the sample space, ensure all combinations are included; mistakes often involve confusing order or omitting outcomes.

Question 15

A student spins a spinner with three equal sections labeled A, B, and C, and then flips a coin. Which list shows the complete sample space for this compound event?

$\{A,B,C,H,T\}$
${A H, A T, B$

Question 16

A student flips a coin and then rolls a standard number cube (1–6). The outcomes can be written like H4 (heads then 4) or T2 (tails then 2). Which set shows the outcomes for the event “heads and an even number”?

{H2, H4, H6, T2, T4, T6}
{H2, H4, H6}
{H1, H3, H5}
{T2, T4, T6}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coin flips {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches for each possibility, like four paths for two flips. For example, for a coin flip and die roll, the list is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two flips shows branches leading to HH, HT, TH, TT. The correct representation here is choice B, which accurately identifies the outcomes for heads and an even number: H2, H4, H6. Common errors include listing heads with odds as in A, tails with evens as in C, or all evens regardless of coin as in D. When creating a list, systematically combine all outcomes from each event, then filter for the event. For identifying events, translate the language like 'heads and even' to locate and count matching outcomes, avoiding mistakes like misinterpreting 'and' or including extras.

Question 17

A student flips a coin and then rolls a standard six-sided number cube (1–6). How many outcomes are in the event “tails or a 6”?

{HH, HT, TH, TT}

, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping twice yielding 4 paths. To identify events, read the description like 'both heads' as HH or 'at least one' as HH, HT, TH, then locate and count them. For example, a coin and die list is , and 'heads and even' is with probability ; a tree for flipping twice shows HH, HT, TH, TT. The correct count is 7 in choice C, including all 6 tails plus H6 without double-counting T6. Common errors include counting only T6 and H6 as 2 in A, all tails as 6 in B, or total space as 12 in D. When creating a list, systematically combine all possibilities; for tables, use rows and columns; for trees, branch out with paths as outcomes. To identify events, translate the language like 'or' for union, locate matching outcomes, and count them, avoiding mistakes like incomplete unions, wrong event language, confusing overlaps, or miscounting outcomes.

Question 18

A student flips a coin and then rolls a standard six-sided number cube (1–6). Which list shows the complete sample space for this compound event?

$\{H1,H2,H3,H4,H5,H6,T2,T4,T6\}$

Question 19

A student flips a coin and then rolls a standard number cube (1–6). Which list shows the complete sample space for this compound event?

{1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T}
{H1, H2, H3, H4, H5, H6}
{H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
{H, T, 1, 2, 3, 4, 5, 6}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coin flips {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches for each possibility, like four paths for two flips. For example, for a coin flip and die roll, the list is {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two flips shows branches leading to HH, HT, TH, TT. The correct representation here is choice A, which lists all 12 possible outcomes completely and accurately. Common errors include incomplete lists like choice D missing T6, or confusing separate events as in B, or only one side as in C. When creating a list, systematically combine all outcomes from each event, such as 2 coin results times 6 die results. For identifying events, translate the description to locate and count matching outcomes, avoiding mistakes like ignoring order or miscounting possibilities.

Question 20

A student flips a coin twice. The outcomes are written in order (first flip, then second flip). Which set lists all outcomes for the event “at least one head”?

{HT, TH}
{HH, HT, TH}
{HH}
{HH, HT, TH, TT}

Explanation: This question tests representing compound sample spaces with lists, tables, or trees, identifying outcomes from everyday language descriptions. Representations include lists that enumerate all possible outcomes, such as for two coins {HH, HT, TH, TT}, tables in a grid like 6×6 for two dice, or trees with branches, such as for flipping a coin twice yielding 4 paths. For example, a coin flip followed by a die roll has a list {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, and the event 'heads and even' is {H2, H4, H6} with probability 3/12; a tree for two coin flips shows paths HH, HT, TH, TT. The correct representation here is choice C, which includes all outcomes with at least one head: HH, HT, TH. Common errors include only both heads in A, only one head in B, or the full sample space in D. When creating a list, systematically combine outcomes and filter for the event, like excluding TT for 'at least one head.' To identify events, translate phrases like 'at least one' to include all qualifying outcomes and count them; mistakes often involve confusing 'at least' with 'exactly' or omitting ordered variations.

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7th Grade Math Quiz: Represent Sample Spaces For Compound Events

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