Probability worksheet with math problems for students.
A probability worksheet with six questions involving dice, marbles, and real-life scenarios, designed for educational use.
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Show Answer Key & Explanations
Step-by-step solution for: Probability Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Probability Worksheets
Let’s go through each problem one by one. I’ll explain how to solve them step by step, then give you the final answers at the end.
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Problem 1: If you roll a die, what are the chances of rolling a two?
A standard die has 6 sides: numbers 1, 2, 3, 4, 5, and 6.
Only one of those is a “2”.
So, chance = (number of ways to get a 2) ÷ (total possible outcomes)
= 1 ÷ 6
→ Answer: 1/6
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Problem 2: If you roll a die, what is the probability that you will roll an even number?
Even numbers on a die: 2, 4, 6 → that’s 3 numbers.
Total outcomes: 6
Probability = 3 ÷ 6 = 1/2
→ Answer: 1/2
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Problem 3: A bag contains 3 red marbles, 3 blue marbles, and 1 green marble. What is the probability that the marble will be blue?
Total marbles = 3 (red) + 3 (blue) + 1 (green) = 7 marbles
Blue marbles = 3
Probability = 3 ÷ 7
→ Answer: 3/7
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Problem 4: A bag contains 6 numbered tiles: 3, 7, 8, 9, 13, and 15. What is the probability of picking an odd number?
First, list which numbers are odd:
Odd numbers: 3, 7, 9, 13, 15 → that’s 5 numbers
Even numbers: only 8 → 1 number
Total tiles = 6
Probability of odd = 5 ÷ 6
→ Answer: 5/6
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Problem 5: Mr. Jones has half air balloons for kids: Harry, Carla, John, Linda, Helen, Peter, Joey — wait, let me count again.
Wait — the names listed are:
Harry, Carla, John, Linda, Helen, Peter, Joey → that’s 7 names? But it says “half air balloons” — probably meant “has 6 balloons” or maybe typo? Let’s read carefully:
> “Mr. Jones has half air balloons.” → That doesn’t make sense. Probably meant “has 6 balloons” or “has balloons for 6 children”? Wait — looking at the names:
“Harry, Carla, John, Linda, Helen, Peter, Joey” — that’s 7 names. But then it says “he can take one child at a ride with him.” And asks for probability of boy or girl.
Let’s check genders from typical name assumptions (since no other info):
Boys: Harry, John, Peter, Joey → 4 boys
Girls: Carla, Linda, Helen → 3 girls
Total children = 7
But wait — the problem says “half air balloons” — maybe it’s a typo and should be “has 6 balloons”? Or perhaps “has balloons for these children” — but there are 7 names.
Actually, re-reading:
“Mr. Jones has half air balloons. Because the basket is so small he can take one child at a ride with him. Harry, Carla, John, Linda, Helen, Peter, and Joey write their name...”
It lists 7 names. So total = 7 children.
Assuming traditional gender associations:
Boys: Harry, John, Peter, Joey → 4
Girls: Carla, Linda, Helen → 3
So:
Probability of selecting a boy = 4/7
Probability of selecting a girl = 3/7
→ Answers:
Boy: 4/7
Girl: 3/7
*(Note: If your teacher uses different gender assumptions, adjust accordingly — but based on common naming, this is correct.)*
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Problem 6: John and Jackie are rolling a die. John wins if he rolls higher than 4. Jackie wins if she rolls 4 or less. Is this game fair?
Fair means both have equal chance of winning.
John wins if roll > 4 → that’s 5 or 6 → 2 outcomes
Jackie wins if roll ≤ 4 → that’s 1, 2, 3, 4 → 4 outcomes
Total outcomes = 6
John’s chance = 2/6 = 1/3
Jackie’s chance = 4/6 = 2/3
They are NOT equal → Game is not fair
→ Answer: No, the game is not fair because Jackie has a higher chance of winning.
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Final Answer:
1. 1/6
2. 1/2
3. 3/7
4. 5/6
5. Boy: 4/7; Girl: 3/7
6. No, the game is not fair.
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Problem 1: If you roll a die, what are the chances of rolling a two?
A standard die has 6 sides: numbers 1, 2, 3, 4, 5, and 6.
Only one of those is a “2”.
So, chance = (number of ways to get a 2) ÷ (total possible outcomes)
= 1 ÷ 6
→ Answer: 1/6
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Problem 2: If you roll a die, what is the probability that you will roll an even number?
Even numbers on a die: 2, 4, 6 → that’s 3 numbers.
Total outcomes: 6
Probability = 3 ÷ 6 = 1/2
→ Answer: 1/2
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Problem 3: A bag contains 3 red marbles, 3 blue marbles, and 1 green marble. What is the probability that the marble will be blue?
Total marbles = 3 (red) + 3 (blue) + 1 (green) = 7 marbles
Blue marbles = 3
Probability = 3 ÷ 7
→ Answer: 3/7
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Problem 4: A bag contains 6 numbered tiles: 3, 7, 8, 9, 13, and 15. What is the probability of picking an odd number?
First, list which numbers are odd:
Odd numbers: 3, 7, 9, 13, 15 → that’s 5 numbers
Even numbers: only 8 → 1 number
Total tiles = 6
Probability of odd = 5 ÷ 6
→ Answer: 5/6
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Problem 5: Mr. Jones has half air balloons for kids: Harry, Carla, John, Linda, Helen, Peter, Joey — wait, let me count again.
Wait — the names listed are:
Harry, Carla, John, Linda, Helen, Peter, Joey → that’s 7 names? But it says “half air balloons” — probably meant “has 6 balloons” or maybe typo? Let’s read carefully:
> “Mr. Jones has half air balloons.” → That doesn’t make sense. Probably meant “has 6 balloons” or “has balloons for 6 children”? Wait — looking at the names:
“Harry, Carla, John, Linda, Helen, Peter, Joey” — that’s 7 names. But then it says “he can take one child at a ride with him.” And asks for probability of boy or girl.
Let’s check genders from typical name assumptions (since no other info):
Boys: Harry, John, Peter, Joey → 4 boys
Girls: Carla, Linda, Helen → 3 girls
Total children = 7
But wait — the problem says “half air balloons” — maybe it’s a typo and should be “has 6 balloons”? Or perhaps “has balloons for these children” — but there are 7 names.
Actually, re-reading:
“Mr. Jones has half air balloons. Because the basket is so small he can take one child at a ride with him. Harry, Carla, John, Linda, Helen, Peter, and Joey write their name...”
It lists 7 names. So total = 7 children.
Assuming traditional gender associations:
Boys: Harry, John, Peter, Joey → 4
Girls: Carla, Linda, Helen → 3
So:
Probability of selecting a boy = 4/7
Probability of selecting a girl = 3/7
→ Answers:
Boy: 4/7
Girl: 3/7
*(Note: If your teacher uses different gender assumptions, adjust accordingly — but based on common naming, this is correct.)*
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Problem 6: John and Jackie are rolling a die. John wins if he rolls higher than 4. Jackie wins if she rolls 4 or less. Is this game fair?
Fair means both have equal chance of winning.
John wins if roll > 4 → that’s 5 or 6 → 2 outcomes
Jackie wins if roll ≤ 4 → that’s 1, 2, 3, 4 → 4 outcomes
Total outcomes = 6
John’s chance = 2/6 = 1/3
Jackie’s chance = 4/6 = 2/3
They are NOT equal → Game is not fair
→ Answer: No, the game is not fair because Jackie has a higher chance of winning.
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Final Answer:
1. 1/6
2. 1/2
3. 3/7
4. 5/6
5. Boy: 4/7; Girl: 3/7
6. No, the game is not fair.
Parent Tip: Review the logic above to help your child master the concept of basic probability worksheet with answers.
