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The probability scale

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Probability

The probability scale

You cannot be certain whether it will rain tomorrow ā€” but a forecast can say 80%. Probability is how maths puts a number on uncertainty.

Every probability lives between 0 and 10impossibleunlikely0.5even chancelikely1certain1/2 = 0.5 = 50%The same probability, three ways of writing it.Nothing sits below 0 or above 1.
Impossible is 0, certain is 1 ā€” everything else is in between.

Events and outcomes

An EVENT is something that might happen: rolling an odd number, winning a match. The OUTCOMES are the individual results that make it up. The outcomes that give an odd number on a dice are 1, 3 and 5. One event, several possible outcomes.

From 0 to 1

A PROBABILITY is a number from 0 to 1 that says how likely an event is. ā€¢ Impossible ā†’ 0 ā€¢ Certain ā†’ 1 ā€¢ An even chance ā†’ 0.5 Nothing can have a probability below 0 or above 1. A probability of 1.4 is not unlikely ā€” it is meaningless.

The words and the numbers

The probability scale lines the words up with the numbers: 0 ā€”ā€”ā€” impossible low ā€”ā€”ā€” unlikely 0.5 ā€”ā€”ā€” even chance high ā€”ā€”ā€” likely 1 ā€”ā€”ā€” certain The words are useful for describing; the numbers are what you calculate with.

Fraction, decimal or percentage

The same probability can be written three ways. An even chance is 1/2, or 0.5, or 50%. To compare probabilities, put them in the SAME form first. Tigers win with probability 45%. Lions win with probability 4/5. Which is more likely? 4/5 = 0.8 = 80%, and 80% > 45%, so Lions.

Worked examples

Tigers 45% or Lions 4/5?

  1. Put both in the same form.
  2. 4/5 = 0.8 = 80%.
  3. 80% is bigger than 45%.

Answer: Lions are more likely to win

The probability of an impossible event

  1. Rolling a 7 on an ordinary dice cannot happen.
  2. Impossible events sit at the very bottom of the scale.

Answer: 0

The probability of a certain event

  1. Rolling a number less than 7 on an ordinary dice always happens.
  2. Certain events sit at the top of the scale.

Answer: 1

Describing a probability of 0.5

  1. 0.5 is exactly halfway along the scale.
  2. It is as likely to happen as not.

Answer: An even chance

Writing 30% three ways

  1. 30% means 30 out of 100.
  2. As a decimal that is 0.3.
  3. As a fraction, 30/100 = 3/10.

Answer: 30% = 0.3 = 3/10

Five heads in a row ā€” what about the next flip?

  1. The coin has no memory of the earlier flips.
  2. Each flip is still an even chance.

Answer: The probability is still 50%

Where you see this in real life

  • A weather forecast saying 80% chance of rain is a probability. It comes from what happened on many past days that looked like today.
  • Insurance prices are built from probabilities of accidents. The less likely the claim, the cheaper the cover.

Key words

Probability
a number from 0 to 1 saying how likely something is
Event
something that might happen
Outcome
one possible result of an event
Even chance
a probability of 0.5 ā€” as likely as not
Certain
sure to happen, probability 1
Impossible
cannot happen, probability 0
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