Equally Likely Outcomes

Sometimes every possible result of an experiment is equally likely — a fair coin is just as likely to land heads as tails, and a fair die is just as likely to show any of its six faces. When that is true, we don't need to flip or roll anything to find a probability: we just count.

Count how many outcomes make the event happen (the favourable ones), then divide by how many outcomes there are in total:

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

A fair coin has two equally likely faces, one of which is heads, so P(\text{heads}) = \tfrac{1}{2}. A fair die has six equally likely faces, and three of them are even (2, 4, 6), so P(\text{even}) = \tfrac{3}{6} = \tfrac{1}{2}.

When every outcome is equally likely:

the probability of an event is P = \dfrac{\text{favourable}}{\text{total}};
so the whole job is to count carefully — how many outcomes are favourable, and how many there are altogether;
a fair die has 6 equally likely faces, a coin has 2, and a single draw from a bag has one outcome per object in the bag.

Count the favourable faces

Lay out the six faces of a fair die, then highlight the ones that count as "even". Three out of six — that is the probability.