Students practice listing sample spaces using organized lists and curly braces in Activity 4 (examples: {Red, Blue, Green, Yellow}, {1,2,3,4,5,6}, {Heads, Tails}). The student activity includes compound situations (Challenge: a coin is flipped and a spinner with Green and Orange is spun) and the answer key gives the combined sample space {Heads-Green, Heads-Orange, Tails-Green, Tails-Orange}. The lesson also uses tables to represent outcomes and counts (the Spinners activity table with sections, fractions, decimals, percents).

Students encounter the definition of "sample space" in the vocabulary match-up and fill in a sample space for a six-sided die ({1,2,3,4,5,6}). A multiple-choice question asks students to identify the sample space for flipping a coin (Heads, Tails). Students also use tables to record spinner outcomes (Color, Tally, Total) when collecting experimental data.

Students construct sample spaces using organized lists, tables, and set notation (e.g., spinner+coin listed as (R,H),(R,T),(B,H),(B,T),(G,H),(G,T) and S = {...}). Students create and read tables and 3x2 or 4x2 grids in multiple activities (spinner/coin, die/coin, spinner/die). Students draw and use tree diagrams (coin→spinner example with S = {(H,R),(H,B),(T,R),(T,B)} and an unequal-probability tree showing repeated branches) and are repeatedly asked to indicate the desired outcome and count matching outcomes to compute probabilities.

Students map digits or marble colors to outcome categories using clear tables (e.g., Number Assignment for genres, Shelf Breakdown for book types) and record sequences of individual trials in data tables labeled "Numbers Rolled" and "Pulls Until Blue." They run repeated compound trials (rolling until a target outcome appears) and organize trial results in tables, then count and convert frequencies (e.g., count trials with 4 or more rolls and report a fraction/percent). The activities prompt students to list the sequence of outcomes within each trial and to use those organized lists/tables to determine which trials meet a described event (such as "4 or more picks" or "until an Instrumental").

Students are asked to create and use organized lists and tables to show sample spaces (see Problem 8: coin and die table with S = {(H,1),…,(T,6)} and several prompts to list sample spaces for flipping two coins and other compound events). Students are asked to draw and interpret tree diagrams (see Problem 9 image and other tree-diagram prompts showing coin→spinner and spinner→die branches with outcomes like (H,G),(H,O),(T,G),(T,O)). The answer key and problems require students to identify which outcomes compose named events (e.g., identify (H,4) as the outcome for "Heads and a 4," list doubles like (1,1),(2,2),…, and list all outcomes for two-dice or coin-and-die experiments).

Students are instructed in Part 2 to produce a full sample space listing all 30 sex×size×color combinations, to fill two organized tables (Sample Space: Male Dogs and Sample Space: Female Dogs), and to draw a tree diagram that branches by sex, then size, then color. The Answer Key provides an explicit list of all 30 ordered outcomes and shows completed tables and a tree diagram. In later parts students use those sample-space representations to compute probabilities and to identify which outcomes compose events (e.g., summing all medium-size outcomes to answer "total probability of meeting a medium-sized dog" and using small/large black outcomes in the simulation).

Students turn raw paired outcomes into organized lists and two-way frequency tables (Activity 3) and fill in cells and totals. Students read and interpret table cells as specific joint outcomes (e.g., "12 students own both a cat and a dog," "how many students own a dog but don't own a cat?" in Activity 2). Students compute relative frequencies from those tables and use them as probabilities (e.g., 18/90 = 0.20 for bikers catching a cold in Activity 4).

Students are asked to list complete sample spaces for compound events such as a coin flip plus a four-section spinner and a coin flip plus a die (e.g., (H,A),(H,B),... and (H,1) through (T,6)). Students are asked to draw tree diagrams for a spinner with 3 red and 2 blue sections combined with a coin and use the diagram to count total outcomes and compute probabilities (e.g., probability of Red and Heads). Student prompts include identifying outcomes that make up events described in everyday language, such as "Heads and C," "Tails and 4," and outcomes that sum to 9 for two dice, with answer keys enumerating the sample spaces.

Students are asked to list the sample space for flipping one coin and spinning a 4-section spinner (question 41) and the answer key shows the organized list {H,A}, {H,B}, {H,C}, {H,D}, {T,A}, {T,B}, {T,C}, {T,D}. Students are asked to draw a tree diagram for a spinner and coin (question 46) and a tree diagram image and prompt appear with follow-up questions about how many outcomes and the probability of red and heads. Students are asked to identify outcomes composing compound events in everyday language (e.g., "tails and landing on C" in question 42 and "red and heads" in question 46) and to compute probabilities from those outcomes.