Basic Probability Calculator

P(E) = n(E) / n(S)

Calculate the probability of an event by dividing favorable outcomes by total possible outcomes.

What is Probability?

Probability is a measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where:

P(E) = n(E) / n(S)

P(E) = Probability of event E occurring

n(E) = Number of favorable outcomes (ways the event can happen)

n(S) = Total number of possible outcomes (sample space)

The set of all possible outcomes of an experiment. For a 6-sided die, S = {1, 2, 3, 4, 5, 6}.

The outcomes that satisfy the condition we are interested in. If we want an even number, favorable outcomes = {2, 4, 6}.

A specific outcome or set of outcomes. "Rolling an even number" is an event.

For basic probability, we assume all outcomes have the same chance of occurring (like a fair die or fair coin).

Problem

What is the probability of rolling an even number on a fair 6-sided die?

Identify the sample space

S = {1, 2, 3, 4, 5, 6}, so n(S) = 6

Count favorable outcomes

Even numbers = {2, 4, 6}, so n(E) = 3

Apply the formula

P(E) = n(E) / n(S) = 3 / 6 = 1/2 = 0.5 = 50%

Answer

The probability of rolling an even number is 1/2 or 50%.