Sample Spaces Worksheets - Free Printable

Since I can’t see or process uploaded images, I’ll solve the problem based on the text you pasted, which appears to be a worksheet titled “Sample Spaces Worksheet 2.” It contains 10 probability problems asking for sample spaces.

Let’s go through each question one by one and list the sample space (the set of all possible outcomes) for each scenario.

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1. A magician asks someone in the audience to roll a die and select two coins from a bag containing 1 nickel, 1 dime, and 1 quarter. List the sample space for both.

→ This is a compound event: rolling a die AND selecting two coins.

- Die outcomes: {1, 2, 3, 4, 5, 6}
- Coin combinations (selecting 2 out of 3 coins — order doesn’t matter):
- Nickel & Dime → ND
- Nickel & Quarter → NQ
- Dime & Quarter → DQ

So the sample space is the Cartesian product:

> {(1,ND), (1,NQ), (1,DQ), (2,ND), (2,NQ), (2,DQ), (3,ND), (3,NQ), (3,DQ), (4,ND), (4,NQ), (4,DQ), (5,ND), (5,NQ), (5,DQ), (6,ND), (6,NQ), (6,DQ)}

Total = 6 × 3 = 18 outcomes.

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2. Henry has a coin, 4 different colored cards and an 8-sided die. List the sample space.

→ Three independent items:
- Coin: {H, T}
- Cards: Let’s call them C1, C2, C3, C4
- Die: {1, 2, 3, 4, 5, 6, 7, 8}

Sample space = all combinations: (Coin, Card, Die)

> {(H,C1,1), (H,C1,2), ..., (T,C4,8)}

Total = 2 × 4 × 8 = 64 outcomes.

You could write it as:

> { (H or T, C1–C4, 1–8) }

But if listing fully is required, it's 64 ordered triples.

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3. A shop has three sizes of random fruit juice containers and any of 4 colors. List the sample spaces.

→ Sizes: say S1, S2, S3
→ Colors: C1, C2, C3, C4

Sample space = all size-color pairs:

> {(S1,C1), (S1,C2), (S1,C3), (S1,C4), (S2,C1), (S2,C2), (S2,C3), (S2,C4), (S3,C1), (S3,C2), (S3,C3), (S3,C4)}

Total = 3 × 4 = 12 outcomes.

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4. The digits 1, 2, 3, 4 are printed on 4 slips of paper. List the sample spaces.

→ Assuming we’re drawing ONE slip at random:

> {1, 2, 3, 4}

If drawing TWO slips without replacement (order matters?):

- With order: permutations → 4P2 = 12 outcomes:
(1,2), (1,3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2), (3,4), (4,1), (4,2), (4,3)

- Without order: combinations → 4C2 = 6 outcomes:
{1,2}, {1,3}, {1,4}, {2,3}, {2,4}, {3,4}

The question says “list the sample spaces” — ambiguous, but since it’s just “digits...on slips”, likely single draw unless specified.

✔ Best interpretation: Single draw → {1, 2, 3, 4}

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5. A glass is 7 cubes with 7 different kinds of tiles inside. List the sample spaces.

→ Probably means: there are 7 distinct tiles in a glass, and you pick one.

> {Tile1, Tile2, Tile3, Tile4, Tile5, Tile6, Tile7}

Or if labeled by color/number, e.g., {A,B,C,D,E,F,G}

Assuming “kinds” = distinct types.

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6. Determine the sample space of heads if there are 2 coins tossed consecutively in a fair game. List all 7 different equally likely?

Wait — this seems misphrased. “List all 7 different equally likely?” — but 2 coins have only 4 outcomes.

Possibly typo. Likely meant: “Determine the sample space of heads when 2 coins are tossed.”

Standard sample space for 2 coins:

> {HH, HT, TH, TT}

Number of heads per outcome:
- HH → 2 heads
- HT → 1 head
- TH → 1 head
- TT → 0 heads

So possible number of heads: {0, 1, 2} — only 3 values, not 7.

✘ “7 different equally likely” doesn’t make sense here.

Possibility: Maybe it’s 3 coins? 3 coins → 8 outcomes, 4 heads counts? No.

Or maybe “list all outcomes” — 4 outcomes.

Perhaps it’s a mistake. I’ll assume it’s 2 coins and list the 4 outcomes.

> Sample space: {HH, HT, TH, TT}

And note: there are NOT 7 equally likely outcomes — only 4.

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7. We have 7 marbles of red, blue, green, yellow, purple, orange, and black. List the sample spaces.

→ Drawing one marble:

> {Red, Blue, Green, Yellow, Purple, Orange, Black}

Total = 7 outcomes.

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8. In the above case, there are 4 different suits and 2 colors. List the sample spaces.

Wait — “above case” refers to marbles? But marbles don’t have suits.

This seems like a mix-up. Possibly referring to cards?

Looking back — Q7 was marbles, Q8 says “in the above case” — that doesn’t fit.

Alternative interpretation: Maybe Q8 is separate — about cards?

It says: “4 different suits and 2 colors”

In standard deck: suits = hearts, diamonds, clubs, spades → 4 suits
Colors: red (hearts/diamonds), black (clubs/spades)

But sample space for what? Drawing one card?

If so, sample space = 52 cards — too big to list.

Perhaps it’s asking for suit-color combinations?

Each suit has a color:

- Hearts → Red
- Diamonds → Red
- Clubs → Black
- Spades → Black

So possible (suit, color) pairs:

> {(Hearts, Red), (Diamonds, Red), (Clubs, Black), (Spades, Black)}

Only 4 unique combinations.

If you’re just listing “colors” and “suits” separately:

- Suits: {Hearts, Diamonds, Clubs, Spades}
- Colors: {Red, Black}

But the question says “list the sample spaces” — plural? Or combined?

✔ Best guess: Combined outcomes of suit and color → 4 outcomes as above.

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9. A student is selected from a different history books, one of 4 different math books and one of 3 different science books. List the sample spaces.

→ This is confusingly worded. Probably means: There are multiple books of each type, and a student selects one book total, choosing from:

- History: say H1, H2, ... (but how many? Not specified)
- Math: 4 different → M1, M2, M3, M4
- Science: 3 different → S1, S2, S3

But “a different history books” — probably typo. Maybe “from a collection of history books” — but no count given.

Possibility: Student selects one book from each category? That would be 3 selections.

But sentence says: “selected from a different history books, one of 4... etc.” — unclear.

Alternative reading: Student selects one book total, and there are:

- Some number of history books (unknown),
- 4 math books,
- 3 science books.

Without number of history books, we can’t define sample space.

This might be a typo. Perhaps it’s: “A student selects one book from each of three categories: history (say n books), math (4), science (3).”

But again, n unknown.

Another possibility: “A student is selected from [a group that has] different history books, 4 math books, and 3 science books” — still unclear.

Given ambiguity, I’ll assume it’s selecting one book total, and “different history books” means there are, say, h history books — but since h isn’t given, perhaps it’s a mistake.

Wait — maybe it’s: “A student selects one book from each category” — then sample space is combinations.

Assume: 1 history book (but how many available?), 1 math, 1 science.

Still incomplete.

Perhaps “a student selects one book from a set containing history, math, and science books” — but again, no counts.

This question is flawed as written.

✔ Best attempt: Assume “history books” = 1 type, but multiple copies? Not helpful.

Maybe it’s: There are 3 categories, and student picks one category and then one book.

But no.

I think the intended meaning is: Student picks one book from each subject — so 3 selections.

But sample space would be triplets: (HistoryBook, MathBook, ScienceBook)

If we assume there are, say, 5 history books (arbitrary), then 5×4×3=60 outcomes.

But since not specified, perhaps the question meant:

> “A student selects one book from 4 different math books and one from 3 different science books” — ignoring history?

That doesn’t help.

Given the confusion, I’ll skip or note it’s ambiguous.

But let’s look at Q10 — maybe pattern.

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10. A coin is tossed and one card is selected from a deck of 52 cards. List the sample spaces.

→ Simple compound event.

Coin: {H, T}
Card: 52 cards — e.g., Ace of Hearts, 2 of Hearts, ..., King of Spades

Sample space = all (coin, card) pairs:

> {(H, Ace♥), (H, 2♥), ..., (H, King♠), (T, Ace♥), ..., (T, King♠)}

Total = 2 × 52 = 104 outcomes.

You can describe it as:

> { (Heads or Tails, Any of 52 Cards) }

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## ✔ Final Answers Summary:

1. {(1,ND), (1,NQ), (1,DQ), (2,ND), ..., (6,DQ)} — 18 outcomes
2. All combinations of (H/T, C1-C4, 1-8) — 64 outcomes
3. {(S1,C1), (S1,C2), ..., (S3,C4)} — 12 outcomes
4. {1, 2, 3, 4} (assuming single draw)
5. {Tile1, Tile2, Tile3, Tile4, Tile5, Tile6, Tile7}
6. {HH, HT, TH, TT} — 4 outcomes (note: “7 equally likely” is incorrect)
7. {Red, Blue, Green, Yellow, Purple, Orange, Black}
8. {(Hearts,Red), (Diamonds,Red), (Clubs,Black), (Spades,Black)} — assuming suit-color combo
9. ❗Ambiguous — insufficient info. If forced: assume 1 history book, 4 math, 3 science → sample space = {(H1,M1,S1), ..., (H1,M4,S3)} — 1×4×3=12 if 1 history book. But not specified.
10. {(H, Card1), (H, Card2), ..., (T, Card52)} — 104 outcomes

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📌 Note: For questions with ambiguity (like #6, #8, #9), I’ve made reasonable assumptions based on typical textbook problems. Always clarify wording if possible!

Let me know if you’d like these written in a specific format (e.g., tree diagram, table, set notation) or if you want probabilities calculated too!