Probability worksheet with a spinner and math problems.

Let’s solve each problem step by step.

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Problem 1: Spinner with numbers 1–8

The spinner has 8 equal sections: {1, 2, 3, 4, 5, 6, 7, 8}

Total outcomes = 8

a) Sample space: That’s just all possible outcomes → {1, 2, 3, 4, 5, 6, 7, 8}

b) Event “not even number”

Even numbers in the set: 2, 4, 6, 8 → that’s 4 numbers

So not even = total – even = 8 – 4 = 4 numbers → {1, 3, 5, 7}

c) Probability of not even = (number of favorable outcomes) / (total outcomes) = 4/8 = 1/2

✔ So for Problem 1:
- a) Sample space: {1,2,3,4,5,6,7,8}
- b) Event: {1,3,5,7}
- c) Probability: 1/2

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Problem 2: Letter from word “MISSISSIPPI”

First, let’s count letters in “MISSISSIPPI”

M I S S I S S I P P I

Break it down:

- M: 1
- I: 4 (positions 2,5,8,11)
- S: 4 (positions 3,4,6,7)
- P: 2 (positions 9,10)

Total letters = 1 + 4 + 4 + 2 = 11

We want probability that letter is “I”

Number of I’s = 4

So probability = 4/11

✔ Answer: 4/11

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Problem 3: Square root of 49

√49 = 7 (since 7 × 7 = 49)

So we’re rolling a die and want probability of getting 7.

But a standard die only has faces: 1, 2, 3, 4, 5, 6 → no 7!

So probability of rolling a 7 = 0

Now look at options:

a) P(6) → that’s 1/6
b) P(0) → probability can’t be 0 as an outcome? Wait — actually, P(event) = 0 means impossible event. But here they are asking which expression equals the probability we found (which is 0). So if the answer is 0, then which option gives 0?

Wait — let’s read again:

> The square root of 49 is ___. What is the probability as a coin?

Wait — that doesn’t make sense. Probably typo. Looking back at original image text:

Actually, looking at your uploaded image description, it says:

> 3) The square root of 49 is ___. What is the probability as a coin?

That seems like a mistake. Maybe it meant “as a die”? Because next part shows options with P(6), P(0), etc., and there's a die picture.

Also, in the image, under question 3, it says:

> The square root of 49 is ___. What is the probability as a coin? ← probably typo, should be “die”

And then options:

a) P(6)
b) P(0)
c) P(7)

Since √49 = 7, and you can't roll 7 on a die → probability = 0

Which option represents probability 0? Option b) P(0) — but wait, P(0) usually means probability of outcome 0, which isn’t on a die either. Actually, this is confusing.

Wait — perhaps the question is: “What is the probability of rolling the square root of 49?” → which is 7 → impossible → probability 0.

Then among the choices, which one equals 0? None directly say “0”, but maybe they mean which event has probability 0?

On a die, P(7) = 0, since 7 isn’t on die.

Looking at options:

a) P(6) → 1/6
b) P(0) → undefined or 0? But 0 isn’t on die → also 0
c) P(7) → definitely 0

But both b and c would be 0? Hmm.

Wait — in the image, the options are labeled:

a) P(6)
b) P(0)
c) P(7)

And the correct answer should be the one that matches the probability we calculated, which is 0.

P(7) = 0 → so c) P(7) is the event whose probability is 0.

But the question says: “What is the probability...” — so maybe they want the value, but the options are events.

This is poorly worded, but likely they mean: which of these probabilities equals the probability of rolling √49?

Since √49=7, and P(rolling 7)=0, and P(7)=0, so answer is c) P(7)

Alternatively, if they meant “what is the numerical probability”, then it’s 0, and none of the options are numbers — they are expressions.

Given context, best interpretation: The probability of rolling √49 (i.e., 7) is 0, and among the choices, P(7) is the event that has probability 0.

So answer is c) P(7)

But let me double-check — in some contexts, P(0) might mean something else, but on a die, 0 isn’t a face, so P(0)=0 too. However, typically when we write P(k), k is an outcome on the sample space. Since 0 and 7 are not on die, both have prob 0. But 7 is the actual value we’re checking, so P(7) makes more sense.

Perhaps the question is misprinted, and it should be “what is the probability of rolling the square root of 49?” and then the answer is 0, and they expect us to choose the option that represents that probability — but since options are P(something), and P(7)=0, I think c) is intended.

Wait — looking back at user’s image transcription:

In the image, after question 3, it says:

> a) P(6)
> b) P(0)
> c) P(7)

And earlier, it says “What is the probability as a coin?” — that must be a typo. Probably “as a die”.

Assuming that, and since √49=7, and die doesn’t have 7, probability is 0, and P(7)=0, so answer is c.

But let’s see the other problems to confirm pattern.

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Problem 4: Dual-number?

Options:

a) P(<4)
b) P(>-1)
c) P(7)

“Dual-number” — probably typo. Maybe “double number”? Or “even number”? Not clear.

Looking at die: outcomes 1-6.

If “dual-number” means even number? Even numbers: 2,4,6 → P(even)=3/6=1/2

Check options:

a) P(<4) → outcomes 1,2,3 → 3/6=1/2
b) P(>-1) → all outcomes since min is 1 > -1 → 6/6=1
c) P(7)=0

So if “dual-number” means even, then P(even)=1/2, same as P(<4)

So answer might be a)

But what is “dual-number”? Could be mistranslation. In some contexts, “dual” might mean two, but not clear.

Another possibility: “dual” as in duplicate? Doesn’t fit.

Perhaps it’s “odd number”? Odd:1,3,5 → P=1/2, still same as P(<4)

Or maybe “number less than 4” — but why call it dual?

Wait — in the image, it says “Dual-number?” — perhaps it’s “What is the probability of rolling a number that is dual?” — still unclear.

Maybe it’s a trick, and “dual” refers to something else.

Another idea: in some games, “dual” might mean matching, but here it’s single die.

Perhaps it’s a typo for “even number”. Given that, and since P(even)=1/2 and P(<4)=1/2, answer is a)

I’ll go with that.

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Problem 5: Prime-number?

Prime numbers on die: 2,3,5 → three primes

P(prime) = 3/6 = 1/2

Options:

a) P(>-1) → all 6 outcomes → 1
b) P(=2) → 1/6
c) P(7) → 0

None is 1/2? That can’t be.

Wait — options are:

a) P(>-1)
b) P(=2)
c) P(7)

But P(prime) = 1/2, not matching any.

Unless “prime-number” is misinterpreted.

Primes between 1-6: 2,3,5 — yes, 3 out of 6.

But none of the options give 1/2.

Perhaps the question is different. Let me read again.

In the image: “5) Prime-number?” and options a) P(>-1) b) P(=2) c) P(7)

Maybe “prime-number” means the number 2, since 2 is the only even prime? But that would be P(2)=1/6, which is option b.

But that seems forced.

Another thought: perhaps “prime” here is a typo, and it’s “primary” or something else.

Or maybe it’s “probability of rolling a prime”, and they want which option equals that, but none do.

Unless I miscalculated.

Die: 1,2,3,4,5,6

Primes: 2,3,5 — yes, 3 numbers.

P=3/6=1/2

Options don't include 1/2.

Perhaps the question is “what is the probability of rolling a number that is prime”, and then the answer is not listed, but that can’t be.

Wait — look at the options again. In the image, for question 5, it says:

> a) P(>-1)
> b) P(=2)
> c) P(7)

But perhaps "Prime-number" is not the event, but part of the question. The full question might be: "What is the probability of rolling a prime number?" and then the options are distractors, but we need to calculate it.

But the way it's phrased, it seems like we need to choose from a,b,c.

Perhaps for question 5, "Prime-number" means the number 2, as it's the smallest prime or something.

But let's see question 6.

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Problem 6:

Options:

a) P(>-1)
b) P(not 2)
c) P(not 3)

No specific event given? In the image, it just says "6)" and then the options.

Probably missing the event. Looking back at user's input:

In the initial description, for question 6, it says:

> 6)
> a) P(>-1)
> b) P(not 2)
> c) P(not 3)

But no event specified. Perhaps it's implied from previous or something.

Maybe it's a continuation, but unlikely.

Another possibility: in some worksheets, question 6 might be "what is the probability of not rolling a 2" or something, but here it's not stated.

Perhaps "6)" is for a different event. Let's assume that for question 6, the event is "not rolling a 2", then P(not 2) = 5/6, and option b is P(not 2), so answer b.

Similarly, if event is "not 3", then c.

But without specification, it's hard.

Perhaps from the context, question 6 is standalone, and we need to interpret.

Another idea: perhaps "6)" refers to the number 6, and we need P(6), but options don't have P(6).

Options are P(>-1), P(not 2), P(not 3)

P(6) = 1/6, while P(>-1)=1, P(not 2)=5/6, P(not 3)=5/6

Not matching.

Perhaps the event is "rolling a number greater than 1" or something.

I think there might be typos in the worksheet.

To resolve, let's look at common questions.

For question 5, if "prime-number" means the probability of rolling a prime, which is 1/2, and none of the options match, but perhaps they want us to recognize that P(>-1) =1, etc.

Maybe for question 5, "Prime-number" is a label, and the actual question is to find which probability is correct for some event, but it's not specified.

This is messy.

Let's try to infer from the answers.

Perhaps for question 3, we have √49=7, P(roll 7)=0, and option c) P(7) is the event with probability 0, so answer c.

For question 4, "Dual-number" might mean even number, P=1/2, and P(<4)=3/6=1/2, so a.

For question 5, "Prime-number" might mean the number 2, as it's the only even prime, so P(2)=1/6, option b.

For question 6, perhaps it's "probability of not rolling a 2", so P(not 2)=5/6, option b.

Or "not 3", same thing.

But let's see the options for 6: a) P(>-1) =1, b) P(not 2)=5/6, c) P(not 3)=5/6

If the event is "rolling a number not 2", then b.

Perhaps the event is implied as "rolling a 6" or something.

Another thought: in some contexts, "6)" might mean the sixth question, and the event is given in the stem, but in your transcription, it's cut off.

Looking back at your initial message, for question 6, it says:

> 6)
> a) P(>-1)
> b) P(not 2)
> c) P(not 3)

And before that, question 5 has "Prime-number?", so perhaps for 6, it's "Not 2" or something.

I think for the sake of completing, I'll assume:

- Q3: c) P(7) because P(roll 7)=0
- Q4: a) P(<4) assuming "dual-number" means even or less than 4
- Q5: b) P(=2) assuming "prime-number" means the number 2
- Q6: b) P(not 2) or c) P(not 3), but since both are similar, perhaps b

But let's calculate properly.

Perhaps for Q6, the event is "rolling a number that is not 2", so P(not 2) = 5/6, and option b is P(not 2), so answer b.

Similarly, for Q5, if "prime-number" means the probability of rolling a prime, which is 1/2, and none of the options are 1/2, but P(>-1)=1, P(=2)=1/6, P(7)=0, so no match. Unless "prime-number" is not the event, but the answer choice.

I think there's a formatting issue.

Another idea: perhaps for questions 3-6, the "a) b) c)" are the answers to choose from, and the question is to select which one is correct for the described event.

For Q3: event is rolling √49=7, P=0, and among a) P(6)=1/6, b) P(0)=0 (if we consider 0 not on die), c) P(7)=0, so both b and c are 0, but c is more direct.

In many such tests, P(7) is used for impossible event.

So I'll go with c for Q3.

For Q4: "Dual-number" — let's assume it means "even number", P=1/2, and P(<4)=3/6=1/2, so a.

For Q5: "Prime-number" — primes are 2,3,5, P=1/2, but options don't have 1/2. Perhaps "prime-number" means the number 2, as it's the first prime, so P(2)=1/6, option b.

For Q6: perhaps the event is "not rolling a 2", so P(not 2)=5/6, option b.

Or "not 3", same.

But in the options for Q6, b is P(not 2), c is P(not 3), so if the event is "not 2", then b.

I think that's reasonable.

So summarizing:

1. a) {1,2,3,4,5,6,7,8} b) {1,3,5,7} c) 1/2

2. 4/11

3. c) P(7)

4. a) P(<4)

5. b) P(=2)

6. b) P(not 2) [assuming event is not rolling 2]

For Q6, since no event is specified, but in many worksheets, it might be "probability of not rolling a 2", so I'll go with that.

Final Answers:

1. a) Sample space: {1,2,3,4,5,6,7,8}
b) Event: {1,3,5,7}
c) Probability: \frac{1}{2}

2. \frac{4}{11}

3. c) P(7)

4. a) P(<4)

5. b) P(=2)

6. b) P(not 2)

But for Q6, to be precise, if the event is not specified, it's ambiguous, but based on common questions, I'll assume it's "not 2".

Perhaps "6)" refers to the number 6, and we need P(6), but options don't have it.

Another possibility: in Q6, "6)" might be a typo, and it's for "rolling a 6", then P(6)=1/6, and none of the options are 1/6, since P(>-1)=1, P(not 2)=5/6, P(not 3)=5/6.

So not matching.

Perhaps the event is "rolling a number greater than 1", then P=5/6, and P(not 2)=5/6 or P(not 3)=5/6, so b or c.

I think it's safe to choose b for Q6.

So I'll box the answers as per above.

Final Answer:

1. a) \{1,2,3,4,5,6,7,8\}
b) \{1,3,5,7\}
c) \frac{1}{2}
2. \frac{4}{11}
3. c
4. a
5. b
6. b