Represent Sample Spaces for Compound Events - 7th Grade Math
Card 1 of 25
Identify the outcomes for “sum is $5$” when rolling two dice (ordered pairs).
Identify the outcomes for “sum is $5$” when rolling two dice (ordered pairs).
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$(1,4),(2,3),(3,2),(4,1)$. These are the only pairs where first die + second die = 5.
$(1,4),(2,3),(3,2),(4,1)$. These are the only pairs where first die + second die = 5.
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Identify the event outcomes for “no heads” in two coin flips.
Identify the event outcomes for “no heads” in two coin flips.
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${TT}$. Only TT has zero heads; all others have at least one.
${TT}$. Only TT has zero heads; all others have at least one.
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What does a table show for a compound event sample space?
What does a table show for a compound event sample space?
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Outcomes arranged by rows and columns for two actions. Each row represents one action's choices, columns show the other's.
Outcomes arranged by rows and columns for two actions. Each row represents one action's choices, columns show the other's.
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What is an outcome in a sample space?
What is an outcome in a sample space?
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One specific result of an experiment (one element of the sample space). A single possibility from the complete list of what could happen.
One specific result of an experiment (one element of the sample space). A single possibility from the complete list of what could happen.
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What does an organized list show for a compound event?
What does an organized list show for a compound event?
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Every possible outcome written in a systematic order. Lists help ensure no outcomes are missed or repeated.
Every possible outcome written in a systematic order. Lists help ensure no outcomes are missed or repeated.
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What is the difference between $(H,T)$ and $(T,H)$ in a compound event?
What is the difference between $(H,T)$ and $(T,H)$ in a compound event?
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They are different outcomes because order matters in ordered pairs. First position shows first action, second shows second action.
They are different outcomes because order matters in ordered pairs. First position shows first action, second shows second action.
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Which option correctly represents “or” in an event description?
Which option correctly represents “or” in an event description?
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Outcomes that satisfy at least one condition (union). Either condition (or both) being true makes the outcome count.
Outcomes that satisfy at least one condition (union). Either condition (or both) being true makes the outcome count.
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Which option correctly represents “and” in an event description?
Which option correctly represents “and” in an event description?
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Outcomes that satisfy both conditions at the same time (intersection). Both conditions must be true for the outcome to count.
Outcomes that satisfy both conditions at the same time (intersection). Both conditions must be true for the outcome to count.
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Identify the outcomes for “first is odd and second is even” when rolling two dice.
Identify the outcomes for “first is odd and second is even” when rolling two dice.
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All $(a,b)$ with $a\in{1,3,5}$ and $b\in{2,4,6}$. First die shows 1, 3, or 5; second shows 2, 4, or 6.
All $(a,b)$ with $a\in{1,3,5}$ and $b\in{2,4,6}$. First die shows 1, 3, or 5; second shows 2, 4, or 6.
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What is the sample space of a compound event?
What is the sample space of a compound event?
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The set of all possible outcomes of the combined actions. Includes every result that could happen when multiple actions occur together.
The set of all possible outcomes of the combined actions. Includes every result that could happen when multiple actions occur together.
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Identify the outcomes for “both even” when rolling one die then another (ordered).
Identify the outcomes for “both even” when rolling one die then another (ordered).
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$(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)$. Both dice must show 2, 4, or 6 (the three even numbers).
$(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)$. Both dice must show 2, 4, or 6 (the three even numbers).
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What is the number of outcomes when rolling two standard dice (ordered pairs)?
What is the number of outcomes when rolling two standard dice (ordered pairs)?
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$36$. Six faces on first die times six on second equals $6 imes 6$.
$36$. Six faces on first die times six on second equals $6 imes 6$.
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Identify the outcomes for “at least one $6$” when rolling two dice (ordered pairs).
Identify the outcomes for “at least one $6$” when rolling two dice (ordered pairs).
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All $(6,k)$ or $(k,6)$ for $k=1$ to $6$, counting $(6,6)$ once. Includes all pairs where first is 6 OR second is 6 (or both).
All $(6,k)$ or $(k,6)$ for $k=1$ to $6$, counting $(6,6)$ once. Includes all pairs where first is 6 OR second is 6 (or both).
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What does a tree diagram show for a compound event sample space?
What does a tree diagram show for a compound event sample space?
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Branching choices for each step, ending in all possible outcomes. Each branch represents a choice, paths show combined outcomes.
Branching choices for each step, ending in all possible outcomes. Each branch represents a choice, paths show combined outcomes.
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Identify the sample space when flipping a coin twice (use ordered outcomes).
Identify the sample space when flipping a coin twice (use ordered outcomes).
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${HH,HT,TH,TT}$. First letter shows first flip, second shows second flip result.
${HH,HT,TH,TT}$. First letter shows first flip, second shows second flip result.
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Identify the sample space when rolling a die and flipping a coin (die first).
Identify the sample space when rolling a die and flipping a coin (die first).
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$(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)$. Each pair shows (die result, coin result) for all combinations.
$(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)$. Each pair shows (die result, coin result) for all combinations.
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What is the number of outcomes when flipping a coin twice?
What is the number of outcomes when flipping a coin twice?
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$4$. Two flips with two outcomes each gives $2 imes 2 = 4$.
$4$. Two flips with two outcomes each gives $2 imes 2 = 4$.
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What is the number of outcomes when rolling a die and flipping a coin?
What is the number of outcomes when rolling a die and flipping a coin?
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$12$. Six die faces times two coin sides equals $6 imes 2 = 12$.
$12$. Six die faces times two coin sides equals $6 imes 2 = 12$.
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Identify the event outcomes for “exactly one head” in two coin flips.
Identify the event outcomes for “exactly one head” in two coin flips.
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${HT,TH}$. Only HT and TH have one H each; HH has two, TT has none.
${HT,TH}$. Only HT and TH have one H each; HH has two, TT has none.
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Identify the event outcomes for “at least one head” in two coin flips.
Identify the event outcomes for “at least one head” in two coin flips.
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${HH,HT,TH}$. All outcomes except TT contain at least one head.
${HH,HT,TH}$. All outcomes except TT contain at least one head.
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Identify the outcomes for: roll a die; event is "number less than $3$".
Identify the outcomes for: roll a die; event is "number less than $3$".
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${1,2}$. Only values 1 and 2 are less than 3.
${1,2}$. Only values 1 and 2 are less than 3.
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Identify the outcomes for: choose a letter from ${A,B}$ then a number from ${1,2,3}$.
Identify the outcomes for: choose a letter from ${A,B}$ then a number from ${1,2,3}$.
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${(A,1),(A,2),(A,3),(B,1),(B,2),(B,3)}$. All 6 ordered pairs: 2 letters × 3 numbers.
${(A,1),(A,2),(A,3),(B,1),(B,2),(B,3)}$. All 6 ordered pairs: 2 letters × 3 numbers.
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Identify the number of outcomes for flipping three coins.
Identify the number of outcomes for flipping three coins.
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$8$. Each coin has 2 outcomes: $2 \times 2 \times 2 = 8$ total.
$8$. Each coin has 2 outcomes: $2 \times 2 \times 2 = 8$ total.
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Identify the outcomes for: roll a die; event is "number less than $3$ or a $6$".
Identify the outcomes for: roll a die; event is "number less than $3$ or a $6$".
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${1,2,6}$. Combines outcomes less than 3 (1,2) with the outcome 6.
${1,2,6}$. Combines outcomes less than 3 (1,2) with the outcome 6.
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Identify the outcomes for: flip two coins; event is "exactly one head" (use ordered pairs).
Identify the outcomes for: flip two coins; event is "exactly one head" (use ordered pairs).
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${(H,T),(T,H)}$. One $H$ and one $T$ in either order.
${(H,T),(T,H)}$. One $H$ and one $T$ in either order.
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