Basic Probability

Probability is the chance of an event happening. To find a probability, count the favourable outcomes and divide by the total number of possible outcomes. Give your answer as a fraction, decimal or percentage, unless the question asks for a specific form.

Common mistake: Make sure the total number of outcomes goes on the bottom of the fraction. If there are 9 counters altogether and 4 are green, the probability of green is \(\frac{4}{9}\), not \(\frac{9}{4}\).

Worked example:
A fair spinner has 4 equal sections numbered 1 to 4. Find the probability of landing on 3.
  1. Step 1
    There are 4 possible outcomes.
  2. Step 2
    Only 1 outcome is a 3.
    \[P(3) = \frac{1}{4}\]
Answer:
\[P(3) = \frac{1}{4}\]
Worked example:
A bag contains 5 red counters, 3 blue counters and 2 green counters. Find the probability of picking a counter that is not blue.
  1. Step 1
    Total counters = 5 + 3 + 2 = 10.
  2. Step 2
    Not blue means red or green.
    \[5 + 2 = 7\]
    \[P(\text{not blue}) = \frac{7}{10}\]
Answer:
\[P(\text{not blue}) = \frac{7}{10}\]