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## Probability: Equilikely outcomes

The probability of an event happening is how likely it is to happen or how frequently it happens.

In a perfectly fair world if a die was thrown a five would come up every six throws.  That means that the probability of getting a 5 = $\frac{1}{6}$.

Generally the probability of something happening $=\frac{\text{possible successes}}{\text{possible outcomes}}$

#### Notation

The probability of A happening can be written as P(A).

So P(red) could be what is the probability of getting red?

Examples

What is the probability of rolling a 3 with a die?

There is 1 possible success (getting 3)

There are 6 possible outcomes (1, 2, 3, 4, 5 or 6)

So $P(3)=\frac{1}{6}$

When rolling a die what is the probability of getting a square number?There are 2 possible successes (1 or 4)There are 6 possible outcomes (1, 2, 3, 4, 5 or 6)

So $P(\text{square})=\frac{2}{6}=\frac{1}{3}$

When playing cards what is the probability of getting a red heart?There are 13 possible successes (13 hearts)There are 52 possible outcomes (52 cards in total)

So $P(\text{heart})=\frac{13}{52}=\frac{1}{2}$

A bag contains 5 red discs and 7 blue discs.I take out a red disc and keep it.  What is the probability the next disc is also red?There are 4 successes (there are only 4 red discs left as we have taken one our already)

There are 11 possible outcomes (there are only 11 discs left now)

So $P(\text{red})=\frac{4}{11}$

Important note: Probabilities can only be given as fractions, decimals or percentages

Questions