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Topic

Probability

Probability describes chance. At National 3, use chance words and simple fractions.

Topic explanation

If 3 out of 10 counters are red, the probability of picking red is 310.

Probabilities sit between 0 and 1. They can also be described using words like unlikely, even chance, likely, and certain.

Read the question carefully and count only the outcomes that match what is being asked.

Quick methods

Probability fraction
Use favourable outcomes over total outcomes.
Impossible
A probability of 0 means it cannot happen.
Certain
A probability of 1 means it must happen.
Total outcomes
Count all the possible results.

Worked examples

Example 1

A bag has 2 red counters and 3 blue counters. What is the probability of picking a red counter?

  1. There are 2 red counters.
  2. There are 2 + 3 = 5 counters in total
  3. Probability = red counters divided by total counters

So: The probability is 25.

Example 2

A fair spinner has 8 equal sections. 3 sections are green. What is the probability of landing on green?

  1. There are 3 green sections.
  2. There are 8 equal sections altogether.
  3. Use favourable outcomes over total outcomes.

So: The probability is 38.

Example 3

A spinner has 4 equal sections. One section is blue. What is the probability of landing on blue?

  1. There is 1 blue section.
  2. There are 4 sections altogether.
  3. Write favourable outcomes over total outcomes.

So: The probability is 14.

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