Maths Olympiad · topic 24 of 33 · free

Probability basics — Maths Olympiad practice

Probability measures how likely something is, as a fraction from 0 to 1. List the equally likely outcomes, count the ones you want, and divide. Olympiad options include the classic slips: comparing favourable with unfavourable, or treating “0, 1 or 2 heads” as equally likely.

How to solve it

Favourable over total — “count what you want, count everything, divide”

  1. Probability = number of favourable outcomes ÷ total number of equally likely outcomes.
  2. List the outcomes: a dice has 6, two coins have 4 (HH, HT, TH, TT), three coins have 8, two dice have 36.
  3. Write the answer as a fraction in its lowest terms; a probability is never more than 1.

Use it for: Dice, coin, card-free bag and spinner questions in Class 7–10 papers and the probability chapter.

Worked example: A bag has 3 red, 5 green and 2 blue balls. One ball is taken out without looking. What is the probability that it is green? 1/2

  1. Total balls: 3 + 5 + 2 = 10.
  2. There are 5 green balls, so the probability is 5/10 = 1/2.

Check: Red 3/10 + green 5/10 + blue 2/10 = 10/10 = 1 — all the chances add up to 1 ✓

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🖨️ Probability Worksheet for Class 8 Maths Olympiad

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