Probability

A number between 0 and 1 measuring how likely an event is to occur.

Venn diagram — two events A and B

Definition

Probability is a number between 0 and 1 that measures how likely an event is to occur.

For equally likely outcomes, probability is:

P(\text{event}) = \frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}

Rolling a die

A fair six-sided die has 6 equally likely outcomes: 1, 2, 3, 4, 5, 6.

Definition

The complement of an event $A$ is the event that $A$ does not happen, written $A^c$ .

P(A^c) = 1 - P(A)

Using the complement

What is the probability of not rolling a 6?

P(\text{not 6}) = 1 - P(\text{6}) = 1 - \frac{1}{6} = \frac{5}{6}

Try it

A bag contains 3 red, 5 blue, and 2 green marbles. You draw one at random. Find: (a) $P(\text{red})$ (b) $P(\text{not green})$

Solution

Total = 10. (a) $P(\text{red}) = \frac{3}{10}$ (b) $P(\text{not green}) = 1 - \frac{2}{10} = \frac{8}{10} = \frac{4}{5}$

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