The probability scale

How likely is that?

• The chance of being struck by lightning in a year is about $0.000001$. The chance of flipping heads is $0.5$. The chance of the sun rising tomorrow is $1$.
• Probability 概率 puts every event on a single scale from impossible ($0$) to certain ($1$).

The probability scale

• $\text{P}(\text{event})$ measures how likely it is, from $0$ to $1$.
• $0$ = impossible, $\dfrac{1}{2}$ = even chance, $1$ = certain.
• Can be written as a fraction, decimal, or percentage.

A fair spinner: eight identical sectors, so each number is an equally likely outcome

Calculating probability

• For equally likely outcomes 结果:

Dice: the probability scale runs from impossible (0) to certain (1)

The complement 补集

• The probability an event does not happen:

Probability runs from $0$ (impossible) to $1$ (certain), with $\tfrac12$ an even chance

Fun fact

• The study of probability began in the 1600s when French gamblers asked mathematicians to solve problems about dice games. Pascal and Fermat's letters founded the whole subject.

The probability scale is a number line from $0$ to $1$ — every event sits somewhere on it.

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