Probability Explorer! 🎲

Probability is the chance that something will happen. We measure it as a number between 0 (impossible) and 1 (certain).

The Probability Scale

0 ¼ ½ ¾ 1
❌ Impossible 😬 Unlikely ⚖️ Even Chance 😊 Likely ✅ Certain
🎯 The Formula:

P(event) = number of favourable outcomes total number of possible outcomes

The Golden Rules of Probability:

⭐ Key Vocabulary: outcome, event, fair, biased, random, theoretical probability, experimental probability, complementary events, sample space

📝 Worked Examples

Study these carefully — they cover every type in Year 6!

Example 1: Coin Flip 🪙

Question: A fair coin is flipped. What is the probability of getting heads?

How to solve: List all possible outcomes: {Heads, Tails} → 2 outcomes total. Heads appears 1 time.

Answer: P(heads) = 12 = 0.5 = 50%

Example 2: Rolling a Die 🎲

Question: A fair six-sided die is rolled. What is the probability of rolling an even number?

How to solve: Possible outcomes: {1, 2, 3, 4, 5, 6} → 6 total. Even numbers: {2, 4, 6} → 3 favourable.

Answer: P(even) = 36 = 12

Example 3: Bag of Marbles 🔮

Question: A bag contains 3 red, 5 blue, and 2 yellow marbles. One is picked at random. What is P(red)?

How to solve: Total marbles = 3 + 5 + 2 = 10. Red marbles = 3.

Answer: P(red) = 310

Example 4: Complementary Events 🔄

Question: The probability of it raining tomorrow is 38. What is the probability it will NOT rain?

How to solve: Use the rule: P(not happening) = 1 − P(happening).
1 − 38 = 88 − 38 = 58

Answer: P(not rain) = 58

🔮 The Marble Bag

Build your own marble bag and watch the probabilities update instantly!

Your bag is empty...
Total: 0

🎲 Die Outcomes Explorer

Which outcomes are favourable? Click a number to highlight it!

1
2
3
4
5
6

P(selected) = 0 / 6

🧩 Drag 1: Coin Flip

A fair coin is flipped. Drag the correct numbers to show P(heads)!

1
2
6
P(heads) =

🧩 Drag 2: Rolling a Die

A fair six-sided die is rolled. Drag the numbers to show P(rolling a 3)!

1
3
6
2
P(rolling a 3) =

🧩 Drag 3: Bag of Marbles

A bag has 3 red and 7 blue marbles. Drag the numbers to show P(red)!

3
7
10
5
P(red) =

💡 Hint: Total marbles = 3 + 7 = ?

🧩 Drag 4: Even Numbers on a Die

A fair die is rolled. The even numbers are {2, 4, 6}. Drag to show P(even)!

2
3
6
4
P(even) =

💡 Hint: How many even numbers are on a die?

🧩 Drag 5: Complementary Events

P(rolling a 6) on a die = 16.
Drag the numbers to show P(not rolling a 6)!

1
5
6
4
P(not 6) = 1 − 16 =

💡 Hint: 1 = 66, so 66 − 16 = ?

🧩 Drag 6: Spinner Challenge

A spinner has 8 equal sections: 3 red, 4 blue, 1 green. Drag the numbers to show P(blue)!

3
4
8
1
P(blue) =

💡 Hint: Total sections = 3 + 4 + 1 = ?

📝 Practice Questions

Grab your paper and pencil! Give all fraction answers in their simplest form.

  1. A fair coin is flipped. What is P(tails)?
  2. A fair six-sided die is rolled. What is P(rolling a 5)?
  3. A bag has 4 red and 6 blue marbles. What is P(red)?
  4. A fair die is rolled. What is P(rolling a number less than 3)?
  5. A bag has 5 green marbles only. What is P(green)?
  6. What is the probability of an impossible event?
  7. A spinner has 8 equal sections: 3 red, 5 blue. What is P(red)?
  8. A bag has 2 red, 3 blue, 5 green marbles. What is P(blue)?
  9. A die is rolled. What is P(rolling an odd number)?
  10. P(heads) = 12. What is P(not heads)?
  11. A die is rolled. What is P(not rolling a 6)?
  12. A bag has 7 red and 3 blue marbles. What is P(blue)?
  13. A spinner has 6 equal sections: 1 red, 2 blue, 3 green. What is P(green)?
  14. A bag has 10 marbles: 4 red, 3 blue, 3 yellow. What is P(yellow)?
  15. Write as a decimal: P(rolling an odd number) on a fair die.
  16. A class has 15 boys and 10 girls. A name is chosen at random. What is P(boy)?
  17. P(event) = ¾. What is P(event NOT happening)?
  18. A bag has 6 marbles: 2 red, 2 blue, 2 green. What is P(not green)?
  19. A die is rolled. What is P(rolling a 7)?
  20. A spinner has 5 equal sections. What is the probability of landing on any one section?
  1. 12
  2. 16
  3. 410 = 25
  4. 26 = 13 (numbers less than 3 are: 1, 2)
  5. 1 (it is certain)
  6. 0
  7. 38
  8. 310
  9. 36 = 12 (odd numbers: 1, 3, 5)
  10. 12
  11. 56
  12. 310
  13. 36 = 12
  14. 310
  15. 0.5
  16. 1525 = 35
  17. 14
  18. 46 = 23
  19. 0 (impossible — a standard die only goes up to 6)
  20. 15

🔥 The Hard Challenge

Show all your working — these need careful thinking!

  1. A bag contains 3 red, 5 blue, and 2 yellow marbles. A marble is picked at random. What is the probability of NOT picking yellow? Show your working.
  2. A fair die is rolled 60 times. How many times would you expect to roll a 4?
  3. A class of 30 students has 12 who walk to school, 10 who come by bus, and 8 who come by car. If a student is chosen at random, what is the probability they do NOT come by car?
  4. A fair die is rolled. What is the probability of rolling a prime number? (Remember: 1 is not prime.)
  5. A bag has some red and blue marbles. P(red) = 38. If there are 24 marbles in total, how many are red?
  6. Two fair coins are flipped at the same time. List ALL possible outcomes. What is P(getting exactly one head)?
  7. A lucky dip bag has 20 prizes: 5 gold, 8 silver, and 7 bronze. What is the probability of winning gold or silver?
  8. A die is rolled 100 times and lands on 6 exactly 20 times. What is the experimental probability of rolling a 6? Is the die fair?
  9. The probability of winning a game is 0.35. What is the probability of not winning? Give your answer as a percentage.
  10. A spinner has sections coloured red, blue, green, and yellow — all equal. P(red) = 0.25. If the spinner is spun 200 times, how many times would you expect it to land on blue?
  1. Total = 10. P(yellow) = 2/10. P(not yellow) = 1 − 2/10 = 8/10 = 4/5.
  2. P(rolling a 4) = 1/6. Expected = 60 × 1/6 = 10 times.
  3. P(car) = 8/30. P(not car) = 1 − 8/30 = 22/30 = 11/15.
  4. Primes on a die: {2, 3, 5} → 3 primes out of 6. P(prime) = 3/6 = 1/2.
  5. 3/8 of 24 = 3 × 3 = 9 red marbles.
  6. Outcomes: {HH, HT, TH, TT}. Exactly one head: {HT, TH} → P = 2/4 = 1/2.
  7. Gold + silver = 5 + 8 = 13. P(gold or silver) = 13/20.
  8. Experimental P(6) = 20/100 = 1/5. Theoretical is 1/6, so the die appears biased towards 6.
  9. P(not winning) = 1 − 0.35 = 0.65 = 65%.
  10. Since all sections are equal and P(red) = 0.25 = 1/4, there are 4 equal sections so P(blue) = 1/4. Expected = 200 × 1/4 = 50 times.
Created by Mr Josh · Year 6 UK Maths Curriculum