Grade 6 Probability Worksheet Sample

Let’s solve each part step by step.

---

Exercise 1: Dice

We’re dealing with a standard six-sided die (numbers 1 to 6).

Total possible outcomes when rolling one die = 6 → {1, 2, 3, 4, 5, 6}

---

1.1 What is the probability that when you roll a numbered 1 through 6 die, the number will be:

a) a six
→ Only one outcome is “six” → favorable outcomes = 1
→ Probability = 1/6

b) even
→ Even numbers on die: 2, 4, 6 → 3 outcomes
→ Probability = 3/6 = 1/2

c) odd
→ Odd numbers: 1, 3, 5 → 3 outcomes
→ Probability = 3/6 = 1/2

d) smaller than 3
→ Numbers smaller than 3: 1, 2 → 2 outcomes
→ Probability = 2/6 = 1/3

---

1.2 What are all the possible outcomes for throwing two dice?

When you throw two dice, each die can show 1 to 6.

So total combinations = 6 × 6 = 36

But the question says: “What are all the possible outcomes... number: ___ or ___ or ___”

Looking at the blank format and context, it seems they want the *possible sums* when rolling two dice.

Minimum sum = 1+1 = 2
Maximum sum = 6+6 = 12

So possible sums: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

That’s 11 different possible sums.

The blanks say: “___ or ___ or ___” — probably expecting three examples? But since it says “all the possible outcomes”, maybe list them all? But there are only 3 blanks shown.

Wait — looking again: “What are all the possible outcomes for throwing [two] dice? Number: ___ or ___ or ___”

This is ambiguous. But in many Grade 6 contexts, when they say “outcomes” for two dice without specifying, they might mean the *sums*. And since there are 3 blanks, perhaps they just want 3 example sums? But that doesn’t make sense for “all”.

Alternatively, maybe they mean the individual results per die? Like first die shows X, second shows Y? But then it would be pairs.

Given the phrasing “number: ___ or ___ or ___”, I think they expect the range of possible *sums*, and since there are 3 blanks, perhaps they want min, middle, max? Or maybe it's a typo and should have more blanks.

But let’s look at common curriculum: In Grade 6, for two dice, often they ask for possible sums. The possible sums are from 2 to 12 inclusive.

Since only 3 blanks are given, and the instruction says “or ___ or ___”, perhaps they want three representative values? But that’s not “all”.

Wait — re-reading: “What are all the possible outcomes for throwing [two] dice? Number: ___ or ___ or ___”

Actually, looking at the image layout, it might be cut off. But based on standard problems, I believe they want the possible *sums*, and since there are 11, but only 3 blanks, perhaps it’s an error. However, in some worksheets, they might accept listing a few as examples.

But to be safe, let’s assume they want the full set. Since we can’t write 11 things in 3 blanks, perhaps the question intends for us to list the minimum, maximum, and one in between? That’s speculative.

Alternative interpretation: Maybe “outcomes” here means the result on each die separately? So for two dice, outcomes could be like (1,1), (1,2)... but again, too many.

Another thought: Perhaps they mean the possible numbers that can appear on a single die? But that’s for one die, and this is Exercise 1.2 after talking about rolling one die in 1.1.

Looking back at 1.1: “when you roll a numbered 1 through 6 die” — so one die.

Then 1.2: “throwing [two?] dice” — the word “two” is partially covered, but from context and the picture of two dice, it’s two dice.

In many textbooks, for two dice, “possible outcomes” refers to the sum.

And since the answer format has three blanks separated by “or”, perhaps they want three example sums? But that doesn't satisfy “all”.

I recall that sometimes they ask: “what are the possible totals?” and list 2, 3, ..., 12.

Given the constraints, and since this is Grade 6, I’ll go with listing the smallest, largest, and most common (which is 7).

But let’s check online or standard answers — actually, no, I must reason.

Perhaps the question is misphrased, and they mean for one die? But 1.1 was one die, 1.2 likely two.

Another idea: “outcomes” might mean the face values that can come up, which for two dice are still 1 to 6, same as one die. But that seems redundant.

Let’s look at the next part: 1.3 talks about “an eight” and “odd number” — which for two dice makes sense (sum of 8, or odd sum).

So yes, for two dice, we consider sums.

For 1.2, since it says “all possible outcomes” and gives three blanks, I think it’s a formatting issue. Probably, they expect students to know that sums range from 2 to 12, and perhaps write 2, 7, 12 as examples? But that’s not accurate.

To resolve this, I’ll provide the complete set in reasoning, but for the answer, since only three blanks, I'll put 2, 7, 12 as representative, but note that all sums from 2 to 12 are possible.

But let's see the exact wording: “What are all the possible outcomes for throwing [two] dice? Number: ___ or ___ or ___”

Perhaps "number" refers to the sum, and they want the possible values, and since there are many, maybe it's a mistake. In some versions, it might have more blanks.

Given that, and to match the format, I'll list three: 2, 7, 12 — but that's incomplete.

Better approach: In probability, for two dice, the possible sums are 2 through 12, so 11 possibilities. But for the answer, since the blank has "or" three times, perhaps they want any three? But the question says "all".

I think there might be a typo in the worksheet. For accuracy, I'll state that the possible sums are 2,3,4,5,6,7,8,9,10,11,12, but for the blank, I'll fill with 2, 3, 4 as starting points? No.

Let's move to 1.3 for clue.

1.3 On the probability scale below, indicate the probability of the following outcomes: (Write the letter on the scale.)

A: An eight — for two dice, sum of 8 is possible. How many ways? (2,6),(3,5),(4,4),(5,3),(6,2) — 5 ways out of 36, so probability 5/36 ≈ 0.138, which is unlikely, closer to "no chance" but not quite. On a scale from no chance to certain, with even chance in middle, 5/36 is less than 0.5, so left of center.

B: An odd number — sum is odd. For two dice, sum is odd if one die even, other odd. Number of ways: 3 even * 3 odd + 3 odd * 3 even = 9 + 9 = 18 ways. Total 36, so 18/36 = 1/2 = even chance.

So B is exactly at "even chance".

A is 5/36 ≈ 13.9%, which is unlikely, so between "no chance" and "even chance", closer to no chance.

But for 1.2, back to it.

Perhaps "outcomes" means the individual results, like the numbers that can appear, which are 1,2,3,4,5,6 for each die, but for two dice, the set of possible numbers is still 1-6.

But that seems odd.

Another interpretation: "outcomes" for throwing two dice could mean the pair, but again, too many.

I recall that in some curricula, for two dice, they ask for the possible sums, and list them.

Given the three blanks, and to proceed, I'll assume they want the minimum, maximum, and median or something. Min=2, max=12, median of sums is 7.

So I'll go with 2, 7, 12 for the blanks.

But let's confirm with calculation.

For now, I'll put that in reasoning.

---

Exercise 2: Deck of cards

Standard deck has 52 cards, but the problem says "deck of 54 cards" — so includes 2 jokers.

Total cards = 54

Colors: usually 26 red, 26 black, plus 2 jokers (often considered colorless or separate).

Suits: Hearts, Diamonds (red), Spades, Clubs (black) — 13 each, so 26 red, 26 black.

Jokers: typically 2, not assigned to suit or color.

So:

- Black cards: 26 (Spades and Clubs)
- Red cards: 26 (Hearts and Diamonds)
- Spades: 13
- Jokers: 2

Now,

2.1 What is the probability that when you draw a card from a deck of 54 cards, it will be:

a) a black card
→ 26 black cards
→ Probability = 26/54 = 13/27

b) a red card — wait, the option is cut off. Looking at the image: "b) t" — probably "a red card"? But in text it says "b) t", might be "a heart" or something. Let's see.

In the user input: "b) t" — likely a typo or cut off. From context, probably "a red card" or "a heart".

Looking at the options: a) black card, b) ? , c) a Spade, d) a Joker

And in the image, it might be "b) a red card" but written as "t" by mistake? Or "b) a ten"? Unlikely.

Perhaps "b) a face card" but not specified.

Another possibility: in some decks, but I think it's "a red card". To be precise, let's assume based on standard.

In the initial description, it says "b) t" — but in the image, it might be clear. Since I can't see, I'll infer from common questions.

Typically, after black card, they ask for red card.

Moreover, in 2.2, it asks for "a card with the number 5", so likely b) is "a red card".

I'll assume b) is "a red card".

So:

b) a red card → 26 red cards → 26/54 = 13/27

c) a Spade → 13 spades → 13/54

d) a Joker → 2 jokers → 2/54 = 1/27

2.2 What is the probability of drawing a card with the number 5 from a deck of 54 cards?

Number 5: in each suit, there is a 5. Suits: Hearts, Diamonds, Spades, Clubs — so 4 fives.

Jokers don't have numbers, so not included.

So 4 cards with number 5.

Probability = 4/54 = 2/27

---

Now, back to 1.2.

After careful thought, I believe for two dice, the possible sums are 2 through 12, and since the worksheet has three blanks, it might be an error, but in many similar worksheets, they expect students to list the range or key values.

Perhaps "outcomes" means the possible numbers on a single die, but that doesn't fit.

Another idea: when throwing two dice, the outcome is the pair, but the "number" might refer to the sum, and they want the possible sums listed, but with only three blanks, perhaps it's for a different question.

Looking at the user input: "1.2 What are all the possible outcomes for throwing [two] dice? Number: ___ or ___ or ___"

And in the image, there is a picture of two dice, so definitely two dice.

I recall that in some contexts, "outcomes" for two dice means the sum, and they might ask for the minimum, maximum, and most likely, but "all" suggests otherwise.

To resolve, I'll provide the complete list in reasoning, and for the answer, since the format requires filling blanks, I'll put 2, 7, 12 as the most representative.

But let's calculate how many ways for each sum to verify.

Sum 2: 1 way (1,1)

Sum 3: 2 ways (1,2)(2,1)

Sum 4: 3 ways

Sum 5: 4 ways

Sum 6: 5 ways

Sum 7: 6 ways

Sum 8: 5 ways

Sum 9: 4 ways

Sum 10: 3 ways

Sum 11: 2 ways

Sum 12: 1 way

All sums from 2 to 12 are possible.

For the answer, I'll write 2, 3, 4 as the first three, but that's arbitrary.

Perhaps the question is for one die? But 1.1 was one die, and 1.2 says "throwing" which might imply two, but in English, "throwing a die" is singular, "dice" plural.

The text says "throwing [blank] dice" — in the image, it might be "two".

Given the ambiguity, and to match the three blanks, I'll assume they want three example sums, say 2, 7, 12.

But for accuracy, in the final answer, I'll list the possible sums as 2 through 12, but since the format has three blanks, I'll use 2, 7, 12.

Let's see the answer format required.

Perhaps for 1.2, "outcomes" means the face values that can appear, which are 1,2,3,4,5,6, and they want three of them? But that doesn't make sense.

Another thought: in some definitions, for two dice, the outcome is the combination, but the "number" might be the sum, and they want the possible values, and since there are 11, but the blank has "or" three times, perhaps it's a mistake, and it should be for one die.

Let's read 1.1: "when you roll a numbered 1 through 6 die" — so one die.

1.2: "throwing [ ] dice" — likely "two" based on picture.

But in the text provided by user, it's "throwing [blank] dice", and in image, it's probably "two".

I think I have to make a decision.

Upon second thought, in many Grade 6 worksheets, for two dice, when they say "possible outcomes" for the sum, they list them as 2,3,4,5,6,7,8,9,10,11,12, and if there are only three blanks, it might be for a different part.

Perhaps "number" refers to the result on the dice, and they want the possible numbers, which are 1 to 6, and they want three examples.

But that seems weak.

Let's look at 1.3: it has "An eight" which is a sum, so for two dice, sums are used.

For 1.2, I'll go with the possible sums being 2, 3, 4, ..., 12, and for the answer, since three blanks, I'll put 2, 7, 12.

So for 1.2: 2 or 7 or 12

But to be precise, let's box the answers as per calculation.

Final decisions:

1.1
a) 1/6
b) 1/2
c) 1/2
d) 1/3

1.2 Possible sums for two dice: 2,3,4,5,6,7,8,9,10,11,12. For the blanks, I'll use 2, 7, 12 as representative.

1.3
A: An eight — probability 5/36 ≈ 0.138, so on the scale, it's unlikely, between "no chance" and "even chance", closer to no chance. Typically, on a line from 0 to 1, 0.138 is about 1/7 of the way, so left side.

B: An odd number — probability 1/2, so exactly at "even chance".

So for A, place it left of center, for B at center.

But since it's "write the letter on the scale", in the answer, we can describe.

2.1
a) 26/54 = 13/27
b) Assuming "a red card": 26/54 = 13/27
c) 13/54
d) 2/54 = 1/27

2.2 4/54 = 2/27

Now for the final answer, I need to provide the answers as per the blanks.

Since the user didn't specify which parts to answer, but the whole exercise, I'll provide all.

But in the response, for Final Answer, I should list the answers for each subquestion.

Also, for 1.2, to be accurate, I'll state that the possible sums are from 2 to 12, but for the blank, use 2, 7, 12.

Perhaps the question is: "What are all the possible outcomes for throwing two dice?" and then "Number: " might be for the sum, and they want the range, but with three blanks, it's odd.

Another idea: "outcomes" might mean the product or something, but unlikely.

I recall that in some contexts, for two dice, the possible outcomes are the pairs, but the "number" might be the sum, and they want the possible sums listed, and since there are 11, but the worksheet has only three blanks, perhaps it's a different question.

Let's count the blanks in 1.2: "___ or ___ or ___" — three blanks.

In 1.1, there are four parts, each with a blank.

For 1.2, perhaps they mean the possible numbers on a single die, but that would be 1,2,3,4,5,6, and they want three of them? But why.

Perhaps "throwing dice" means rolling one die, but the picture shows two, and 1.3 has "an eight" which requires two dice.

I think I have to conclude that for 1.2, the intended answer is the possible sums, and since only three blanks, it's likely a formatting error, but for the sake of answering, I'll put 2, 3, 4 as the first three possible sums.

Or perhaps 2, 12, and 7.

I'll go with 2, 7, 12 as min, mode, max.

So for 1.2: 2 or 7 or 12

Now for the final answer section, I'll list all answers.

Also, for 1.3, since it's to mark on a scale, in text, I can say A is near "no chance", B at "even chance".

But for the answer, perhaps just state the positions.

Since the user may expect numerical answers for probabilities, and for 1.3, descriptive.

But in the final answer, I'll provide what can be boxed.

Let's compile.

First, for 1.1:
a) \frac{1}{6}
b) \frac{1}{2}
c) \frac{1}{2}
d) \frac{1}{3}

For 1.2: 2, 7, 12 (as representatives)

For 1.3: A is unlikely (left of center), B is even chance (center)

For 2.1:
a) \frac{13}{27}
b) \frac{13}{27} (assuming red card)
c) \frac{13}{54}
d) \frac{1}{27}

For 2.2: \frac{2}{27}

Now, to confirm 2.1 b): in the user input, it's "b) t" — but in the image, it might be "a red card". If it's "a ten", then number 10: there are 4 tens (one per suit), so 4/54 = 2/27, but that would be unusual after black card.

If "b) a face card", face cards are Jack, Queen, King — 3 per suit, 4 suits, so 12 face cards, probability 12/54 = 2/9.

But "t" might be "ten" or "two" etc.

In the initial problem statement, it's "b) t" — likely a typo, and from context, probably "a red card".

To be safe, I'll assume "a red card" as it's symmetric to a) black card.

So I'll proceed.

Final Answer will include all.

But for the response, since ExplainAnswer is false, TeachTopic false, GeneratePractice false, I only provide Final Answer.

So I need to box the answers.

Perhaps list them as:

1.1 a) \frac{1}{6} b) \frac{1}{2} c) \frac{1}{2} d) \frac{1}{3}

1.2 2, 7, 12

1.3 A: unlikely (left of even chance), B: even chance

2.1 a) \frac{13}{27} b) \frac{13}{27} c) \frac{13}{54} d) \frac{1}{27}

2.2 \frac{2}{27}

For 1.2, to be precise, the possible sums are 2 through 12, but for the blank, I'll use 2, 7, 12.

Some might argue that for two dice, the outcomes are the pairs, but the "number" suggests sum.

I think it's fine.

So Final Answer: