# Probability for Equally Likely Outcomes Calculator

Posted by Dinesh on

The outcomes of an experiment are equally likely to occur when the probability of each outcome is equal.
For any sample space with N equally likely outcomes, we assign the probability $\frac{1}{N}$ to each outcome.

#### Examples of experiments with equally likely outcomes are:

• Draw a random sample of size n from a population or urn. The assumption that the sample is drawn at random means that all samples of size n have an equal chance of being chosen (much of statistical analysis depends on the assumption that samples are chosen randomly).
• Flip a fair coin n times and observe the sequence of heads an tails that results.
• Roll n dice, die 1, die 2, die 3, . . . , die n, and observe the ordered sequence of numbers on the uppermost faces.

### Formula:

$\mathrm{P\left(E\right)}=\frac{f}{N}$

where,
f denotes the number of ways event E can occur,
N denotes the total number of outcomes possible,
P(E) denotes probability for equally likely outcomes