Functional Skills Practice

🎲 Maths: Probability

Maths: Probability

Probability measures how likely an event is to happen. It is recorded on a scale running from 0 (impossible) at the left-hand end to 1 (certain) at the right-hand end. An event with an even chance of happening or not happening sits in the middle, equivalent to one half, 0.5 or 50%. Because the number of favourable outcomes can never exceed the total number of outcomes, every probability value lies between 0 and 1 inclusive (0% to 100%). This scale is the Level 1 foundation that underpins all Level 2 probability work.

The language of probability describes these positions. The closer a probability is to 0 the less likely the event; the closer it is to 1 the more likely it is. This justifies descriptive terms such as impossible (0), unlikely (between 0 and 0.5), even chance (0.5), likely (between 0.5 and 1) and certain (1).

For equally likely outcomes, calculate the probability of a single event as the number of favourable outcomes divided by the total number of possible outcomes: P(event) = favourable outcomes / total outcomes. At Level 2 you must express probabilities as fractions, decimals and percentages. These are equivalent ways of writing the same value and can be converted between one another, for example:

The probabilities of all the possible outcomes of an event always add up to 1. It follows that the probability of an event not happening equals 1 minus the probability that it does happen (the complement rule): P(not A) = 1 - P(A). So if the probability of rain is 0.3, the probability of no rain is 0.7.

At Level 2 you must also work out the probability of combined events, using diagrams and tables, including 2-way tables. Listing every possible outcome systematically helps you count the favourable ones correctly. Probability can then be used to make predictions over repeated trials: multiply the probability by the number of trials to estimate how often an event should occur (for example, a probability of 0.25 across 40 trials predicts about 10 occurrences). Always interpret these results sensibly in real-life contexts, remembering that predictions are estimates rather than guarantees.

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Sample questions (35)

1. On the probability scale, which word describes an event that has a probability of 1?

  1. Impossible
  2. Even chance
  3. Certain
  4. Unlikely

A probability of 1 means the event must happen, so it is described as certain and placed at the right-hand end of the scale. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

2. Which word describes an event with a probability of 0?

  1. Certain
  2. Impossible
  3. Likely
  4. Even chance

A probability of 0 means the event cannot happen, so it is described as impossible and placed at the left-hand end of the scale. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

3. The probability scale runs between which two values?

  1. 0 and 1
  2. 1 and 10
  3. 0 and 100
  4. -1 and 1

Probability is measured on a scale from 0 (impossible) to 1 (certain). (DfE/ESFA, Subject content: Functional Skills maths (GOV.UK), Level 1 content statement 26)

4. A fair coin is tossed once. Which word best describes the chance of getting heads?

  1. Impossible
  2. Even chance
  3. Certain
  4. Very unlikely

There are two equally likely outcomes, heads and tails, so heads has an even chance, equivalent to 1/2 or 50%. (Third Space Learning, GCSE Maths: Probability Scale (even chance = 1/2))

5. Which of these events is certain?

  1. Rolling a 7 on an ordinary six-sided dice
  2. Tomorrow being a day of the week
  3. Picking a red ball from a bag of only blue balls
  4. Throwing a fair coin and it landing on its edge

Tomorrow must be one of the seven days of the week, so the event is certain with a probability of 1. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

6. Which of these events is impossible?

  1. Rolling an even number on a six-sided dice
  2. Drawing a queen from a standard pack of cards
  3. Rolling a number greater than 6 on an ordinary six-sided dice
  4. The sun setting this evening

An ordinary dice only has the numbers 1 to 6, so rolling a number greater than 6 cannot happen and has a probability of 0. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

7. An event has a probability of 0.5. Which word describes it?

  1. Impossible
  2. Even chance
  3. Certain
  4. Very unlikely

A probability of 0.5 (equivalent to 1/2 or 50%) sits in the middle of the scale and describes an even chance. (Third Space Learning, GCSE Maths: Probability Scale (even chance = 1/2))

8. An event has a probability of 0.2. Which word best describes how likely it is?

  1. Likely
  2. Certain
  3. Unlikely
  4. Even chance

A probability of 0.2 lies between 0 and 0.5, so the event is unlikely. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

9. An event has a probability of 0.85. Which word best describes how likely it is?

  1. Unlikely
  2. Likely
  3. Impossible
  4. Even chance

A probability of 0.85 lies between 0.5 and 1, so the event is likely. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

10. The weather forecast says there is a 90% chance of rain tomorrow. Which word best describes rain tomorrow?

  1. Impossible
  2. Unlikely
  3. Likely
  4. Even chance

A 90% chance is well above 50%, so rain is likely, although not certain. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

11. Two events are described in words. Which statement is correct about their likelihood?

  1. An event with probability 0.1 is more likely than an event with probability 0.7
  2. An event with probability 0.7 is more likely than an event with probability 0.1
  3. Both events are equally likely
  4. Neither event can happen

The closer a probability is to 1, the more likely the event, so 0.7 is more likely than 0.1. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

12. A bag contains 1 red counter and 19 blue counters. One counter is taken at random. Which word best describes the chance of taking the red counter?

  1. Certain
  2. Likely
  3. Unlikely
  4. Even chance

The probability of red is 1/20 = 0.05, which is close to 0, so taking the red counter is unlikely. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

13. A learner says an event is impossible. What must its probability be?

  1. Exactly 0
  2. Exactly 0.5
  3. Exactly 1
  4. Any value between 0 and 1

An impossible event cannot happen, so its probability is exactly 0. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

14. The probabilities of all the possible outcomes of an event always add up to which value?

  1. 0
  2. 0.5
  3. 1
  4. 100

The probabilities of all possible outcomes of an event always sum to 1. (Third Space Learning, GCSE Maths: Probability Scale ('The chance of all outcomes of an event will always add up to one'))

15. Which formula gives the probability of an event NOT happening?

  1. P(not A) = 1 - P(A)
  2. P(not A) = 1 + P(A)
  3. P(not A) = P(A) - 1
  4. P(not A) = P(A)

Because all outcomes sum to 1, the probability of an event not happening is 1 minus the probability of it happening. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

16. The probability that it rains tomorrow is 0.3. What is the probability that it does NOT rain tomorrow?

  1. 0.3
  2. 0.7
  3. 0.5
  4. 1.3

P(not rain) = 1 - 0.3 = 0.7. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

17. The probability that a bus is late is 0.25. What is the probability that the bus is NOT late?

  1. 0.25
  2. 0.5
  3. 0.75
  4. 0.85

P(not late) = 1 - 0.25 = 0.75. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

18. The probability of winning a game is 1/4. What is the probability of NOT winning?

  1. 1/4
  2. 1/2
  3. 3/4
  4. 4/4

P(not win) = 1 - 1/4 = 3/4. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

19. The probability that a randomly chosen item passes a quality check is 92%. What is the probability that it does NOT pass?

  1. 2%
  2. 8%
  3. 18%
  4. 92%

P(not pass) = 100% - 92% = 8%. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

20. A spinner lands on red with probability 0.4. Red and 'not red' are the only outcomes. What is the probability of landing on 'not red'?

  1. 0.4
  2. 0.5
  3. 0.6
  4. 1.4

Since the two probabilities must sum to 1, P(not red) = 1 - 0.4 = 0.6. (Third Space Learning, GCSE Maths: Probability Scale ('The chance of all outcomes of an event will always add up to one'))

21. The probability of an event happening is 3/5. Which value is the correct probability of it NOT happening, written as a decimal?

  1. 0.6
  2. 0.4
  3. 0.2
  4. 0.5

P(event) = 3/5 = 0.6, so P(not event) = 1 - 0.6 = 0.4. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

22. A weather app shows a 35% chance of snow. A learner needs the probability of NO snow as a fraction in its simplest form. Which is correct?

  1. 35/100
  2. 65/100
  3. 13/20
  4. 7/20

P(no snow) = 100% - 35% = 65% = 65/100, which simplifies to 13/20. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

23. On a probability scale, what value is given to an event that is impossible (cannot happen)?

  1. 0
  2. 1
  3. 0.5
  4. -1

An impossible event is placed at the left-hand end of the scale and has a probability of 0. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

24. What probability value is given to an event that is certain to happen?

  1. 100
  2. 0.5
  3. 1
  4. 0

A certain event is placed at the right-hand end of the scale and has a probability of 1. (Third Space Learning, GCSE Maths: Probability Scale (probability scale endpoints))

25. Between which two values must every probability lie?

  1. 0 and 1 inclusive
  2. 0 and 10
  3. 1 and 100
  4. -1 and 1

Because the favourable outcomes can never exceed the total outcomes, every probability lies between 0 and 1 inclusive (0% to 100%). (Cuemath, Probability — Formula, Calculating, Find, Theorems, Examples (range of probability))

26. An event has an even chance of happening or not happening. Which value best describes its probability?

  1. 0.5
  2. 0
  3. 1
  4. 0.05

An even chance sits in the middle of the scale, equivalent to one half, 0.5 or 50%. (Third Space Learning, GCSE Maths: Probability Scale (even chance = 1/2))

27. Which of these probabilities describes the LEAST likely event?

  1. 0.1
  2. 0.5
  3. 0.8
  4. 0.95

The closer a probability is to 0, the less likely the event is; 0.1 is nearest to 0. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

28. Which of these probabilities describes the MOST likely event?

  1. 0.9
  2. 0.6
  3. 0.4
  4. 0.2

The closer a probability is to 1, the more likely the event is; 0.9 is nearest to 1. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

29. A weather forecast says there is a 0.2 probability of rain tomorrow. Which descriptive term best fits this value?

  1. Unlikely
  2. Likely
  3. Certain
  4. Even chance

A probability between 0 and 0.5 is described as unlikely; 0.2 lies in that range. (Third Space Learning, GCSE Maths: Describing Probability (likelihood descriptors))

30. The probability that a bus arrives on time is given as 75%. Where would this sit on a 0 to 1 scale?

  1. At 0.75, in the 'likely' region
  2. At 0.075, in the 'unlikely' region
  3. At 7.5, beyond the scale
  4. At 0.25, in the 'unlikely' region

75% is equivalent to 0.75, which lies between 0.5 and 1 and is therefore likely. (Third Space Learning, GCSE Maths: Probability Scale (equivalent fraction/decimal/percentage representations))

31. Which probability is equivalent to one quarter?

  1. 0.25 or 25%
  2. 0.4 or 40%
  3. 0.5 or 50%
  4. 0.75 or 75%

One quarter is the same value written as 0.25 or 25%. (Third Space Learning, GCSE Maths: Probability Scale (equivalent fraction/decimal/percentage representations))

32. A learner claims an event has a probability of 1.4. Why must this be wrong?

  1. Probability can never be greater than 1
  2. Probability must always be a fraction
  3. Probability can never be a decimal
  4. Probability must always be below 0.5

Favourable outcomes cannot exceed total outcomes, so every probability lies between 0 and 1; 1.4 is impossible. (Cuemath, Probability — Formula, Calculating, Find, Theorems, Examples (range of probability))

33. The probability of picking a red counter from a bag is 3/5. Written as a decimal and percentage, where does this sit?

  1. 0.6 and 60%, in the 'likely' region
  2. 0.35 and 35%, in the 'unlikely' region
  3. 0.06 and 6%, in the 'unlikely' region
  4. 0.65 and 65%, exactly even

3 divided by 5 is 0.6, which is 60% and lies between 0.5 and 1, so it is likely. (DfE/ESFA, Subject content: Functional Skills maths (GOV.UK), Level 2 content statement 27)

34. The probability of an event happening is 0.35. What is the probability that it does NOT happen?

  1. 0.65
  2. 0.35
  3. 0.55
  4. 1.35

Using the complement rule, P(not A) = 1 - P(A) = 1 - 0.35 = 0.65. (Third Space Learning, GCSE Maths: Probability Scale (complement principle))

35. A spinner can land on green with probability 0.5 or on yellow with probability 0.3. What is the probability it lands on neither green nor yellow?

  1. 0.2
  2. 0.8
  3. 0.5
  4. 0.3

All outcome probabilities sum to 1, so the remaining probability is 1 - 0.5 - 0.3 = 0.2. (Third Space Learning, GCSE Maths: Probability Scale ('The chance of all outcomes of an event will always add up to one'))

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