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Introducing Probability

≈ 20 min
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Probability measures how likely an event is. We describe likelihood in words along a scale:

impossible  →  unlikely  →  even chance  →  likely  →  certain.\text{impossible} \;\to\; \text{unlikely} \;\to\; \text{even chance} \;\to\; \text{likely} \;\to\; \text{certain}.

When all outcomes are equally likely, we can put a number to it as a fraction:

probability=number of favourable outcomestotal number of outcomes.\text{probability} = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}.

Worked examples. A fair coin has 22 equally likely outcomes, so P(heads)=12P(\text{heads}) = \frac{1}{2}. A fair six-sided die has 66 outcomes, so P(rolling a 5)=16P(\text{rolling a }5) = \frac{1}{6}.

Which word best describes the chance that the sun will rise tomorrow?

A fair coin is tossed. What is the probability of getting heads? Give your answer as a fraction, e.g. 1/2.

A fair six-sided die is rolled. What is the probability of rolling a 55? Give your answer as a fraction, e.g. 1/6.

A bag holds 22 red, 11 green and 11 yellow sweet. You take one without looking. Which colour are you most likely to pick?