Maths Library

Theoretical Probability: Year 11 maths

This topic covers quantifying the likelihood of single events using words, probability scales, and numerical values. Pupils practise expressing probabilities as fractions or decimals and calculating complementary outcomes.

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What this covers

Theoretical Probability is taught in Year 11 (age 15 to 16, KS4) as a topic to introduce. It sits in the Probability strand.

Worked example

A bag contains 3 red marbles and 5 blue marbles. What is the probability of picking a red marble at random

  1. Find the total number of possible outcomes: 3 + 5 = 8.
  2. Identify the number of favorable outcomes: 3.
  3. Express as a fraction: 38.

Answer: 38

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Describing likelihood using language (impossible, unlikely, evens, likely, certain)
  2. Calculating simple probabilities as fractions from fair spinners or dice
  3. Calculating probabilities from word problems and simplifying fractions
  4. Calculating the probability of complementary events (1 - P(A))
  5. Solving reverse probability problems to determine counts of items

Common mistakes

  • Writing probability as an odds ratio (favourable : unfavourable) instead of favourable over total outcomes
  • Believing past independent random events influence future outcomes

Curriculum links

Indicative matches to National Curriculum for England. Check wording and codes against the official document.

  • Calculate probabilities of combined events using tree diagrams and sample space methods.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Theoretical Probability

Year 11 maths

Qs
6
Marks
18
NameDateScore / 18
1.
A bag has 5 red and 6 blue counters. One counter is picked at random. What is the probability it is red?
[3]
2.
A bag has 5 red and 5 blue counters. One counter is picked at random. What is the probability it is red?
[3]
3.
A bag has 5 red and 2 blue counters. One counter is picked at random. What is the probability it is red?
[3]
4.
A bag has 1 red and 5 blue counters. One counter is picked at random. What is the probability it is red?
[3]
5.
A bag has 2 red and 6 blue counters. One counter is picked at random. What is the probability it is red?
[3]
6.
A bag has 5 red and 1 blue counters. One counter is picked at random. What is the probability it is red?
[3]

Answer key

  1. 511P(red) = number of red ÷ total = 5/11; Simplified: 5/11
  2. 12P(red) = number of red ÷ total = 5/10; Simplified: 1/2
  3. 57P(red) = number of red ÷ total = 5/7; Simplified: 5/7
  4. 16P(red) = number of red ÷ total = 1/6; Simplified: 1/6
  5. 14P(red) = number of red ÷ total = 2/8; Simplified: 1/4
  6. 56P(red) = number of red ÷ total = 5/6; Simplified: 5/6