Probability
31 free practice questions with explanations
PassNova has 31 free GCSE Maths Foundation practice questions on Probability, each with a clear explanation. Practise them in the browser with instant feedback — 100% free, no sign-up, on any device. Updated for 2026.
Probability: example questions & answers
12 worked examples with answers and explanations below. Practise all 31 Probability questions free in the browser, with instant feedback on every answer.
A fair coin is flipped. What is the probability of getting heads?
- A0
- B0.25
- C0.5✓
- D1
Answer: A fair coin has two equally likely outcomes. P(heads) = 1/2 = 0.5.
A fair die is rolled. What is the probability of getting a 6?
- A1/6✓
- B1/5
- C1/4
- D1/3
Answer: A fair die has 6 equally likely outcomes. P(6) = 1/6.
A bag contains 3 red balls and 2 blue balls. If you pick one at random, what is the probability of picking red?
- A2/5
- B3/5✓
- C1/2
- D3/2
Answer: Total balls = 5. Red balls = 3. P(red) = 3/5.
A fair die is rolled. What is the probability of getting a number greater than 4?
- A1/6
- B2/6✓
- C3/6
- D4/6
Answer: Numbers greater than 4 are 5 and 6. P(>4) = 2/6 = 1/3.
A card is drawn from a standard deck (52 cards). What is the probability of drawing an ace?
- A1/52
- B4/52✓
- C12/52
- D13/52
Answer: There are 4 aces in a deck of 52 cards. P(ace) = 4/52 = 1/13.
A spinner has sections labelled 1, 2, 3, and 4. If you spin it twice, what is the probability of getting two 4s?
- A1/4
- B1/8
- C1/16✓
- D2/16
Answer: P(first 4) = 1/4. P(second 4) = 1/4. P(both 4) = 1/4 × 1/4 = 1/16.
A die is rolled 60 times. The number 3 appears 10 times. What is the relative frequency of rolling a 3?
- A3/10
- B1/60
- C1/10
- D10/60✓
Answer: Relative frequency = (number of times event occurs) ÷ (total number of trials) = 10/60 = 1/6.
If the probability of an event is 0.8, what is the probability it doesn't happen?
- A0.2✓
- B0.8
- C0.5
- D1.8
Answer: P(event doesn't happen) = 1 - P(event) = 1 - 0.8 = 0.2.
Two fair coins are flipped. What is the probability of getting at least one head?
- A1/4
- B1/2
- C3/4✓
- D1
Answer: Possible outcomes: HH, HT, TH, TT. 'At least one head' = HH, HT, TH = 3 outcomes. P = 3/4.
A bag contains 5 red, 3 blue, and 2 green balls. If you draw one at random, what is the probability of drawing green?
- A2/10✓
- B2/5
- C3/10
- D5/10
Answer: Total = 5 + 3 + 2 = 10. Green = 2. P(green) = 2/10 = 1/5.
A die is rolled. What is the probability of getting an even number?
- A1/6
- B1/3
- C1/2✓
- D2/3
Answer: Even numbers on a die: 2, 4, 6. That's 3 out of 6. P(even) = 3/6 = 1/2.
In a class of 30 students, 18 wear glasses. If you pick one student at random, what is the probability they wear glasses?
- A12/18
- B3/5✓
- C12/30
- D1/2
Answer: P(glasses) = 18/30 = 3/5.