Coin Flip Probability

Master coin probability step by step

The Two Possible Outcomes

Heads (H)

Tails (T)

When you flip a fair coin once, there are exactly two possible outcomes: Heads or Tails. Each outcome is equally likely.

The sample space (denoted ) is the set of all possible outcomes of an experiment. For a single coin flip:

The sample space contains two elements: Heads and Tails

The total number of possible outcomes

Equal probability for each outcome

Question

What is the probability of flipping a fair coin and getting Heads?

List all possible outcomes when flipping a coin once:

H = Heads, T = Tails

The total number of outcomes in the sample space:

The event "getting Heads" corresponds to which outcomes?

Only one outcome satisfies "getting Heads"

Answer

==50%

By the same logic:

Favorable outcomes:so

Total outcomes:

Probability:

Key Insight

Notice that . This is always true: the probabilities of all possible outcomes must sum to 1.

Since Heads and Tails are the only two outcomes, they are complements of each other:

This is useful when it is easier to calculate the probability of an event not happening.