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Topic guide · JSS 2, JSS 3, SS 2

Probability

Learn probability step by step: simple probability, the probability of 'not', two dice, and independent events — with an interactive outcome grid.

Start the Probability of Combined Events lesson →

Probability explained

Probability measures how likely something is to happen, on a scale from 0 (impossible) to 1 (certain). If a bag holds 3 red and 5 blue balls, the probability of picking red is 38.

For two events — like throwing two dice — list all the equally likely outcomes, or multiply the probabilities if the events are independent.

Key ideas to remember

  • P(event) = number of favourable outcomes ÷ total number of equally likely outcomes.
  • P(not A) = 1 − P(A).
  • Two dice give 6 × 6 = 36 equally likely outcomes. (1, 6) and (6, 1) are different outcomes.
  • For independent events, P(A and B) = P(A) × P(B).

Worked example

A bag contains 3 red, 2 blue and 6 green balls. A ball is picked at random. What is the probability that it is not blue?

  1. Step 1: Total number of balls

    3 + 2 + 6 = 11

  2. Step 2: Balls that are not blue

    9

  3. Step 3: Probability

    P = 911

Final answer: 911

Practice questions

Have a go, then open the answer to check your working. Every answer was checked by the MathPlug maths engine.

  1. Question 1

    Two fair dice are thrown together. What is the probability that the sum of the numbers is 4?

    • A14
    • B112
    • C111
    • D118
    Show answer and working

    1. Step 1: List the outcomes

      (1,3), (2,2), (3,1)

    2. Step 2: Probability

      336 = 112

    Final answer: 112

  2. Question 2

    The probability that Kemi passes an exam is 12 and the probability that Yusuf passes is 14. Find the probability that both pass.

    • A18
    • B16
    • C38
    • D34
    Show answer and working

    1. Step 1: Multiply

      12 × 14 = 18

    Final answer: 18

  3. Question 3

    A bag contains 7 red, 7 blue and 4 green balls. A ball is picked at random. What is the probability that it is not red?

    • A1118
    • B718
    • C13
    • D719
    Show answer and working

    1. Step 1: Total number of balls

      7 + 7 + 4 = 18

    2. Step 2: Balls that are not red

      11

    3. Step 3: Probability

      P = 1118

    Final answer: 1118

More practice with instant feedback →

Frequently asked questions

Why isn't the probability of a total of 7 with two dice equal to 1/11?
Although there are 11 possible totals (2 to 12), they are not equally likely. Six of the 36 outcomes add to 7, so P(7) = 636 = 16.
Can a probability be bigger than 1?
No. Probabilities are always between 0 and 1. If you get more than 1, check your working.