How to Calculate Probability

The probability of an event is the number of outcomes you care about divided by the total number of equally likely outcomes. Rolling a single die and wanting a four gives one favorable outcome out of six, so the probability is one sixth, or about 0.167. Probability always sits between zero, meaning impossible, and one, meaning certain.

You can express the same value as a fraction, a decimal, or a percentage, and the tool shows all three. The key assumption is that the outcomes are equally likely; if they are not, this simple ratio does not apply and you need weighted probabilities instead.

Two events are independent when the outcome of one has no effect on the other, like flipping a coin and then rolling a die. For independent events, the probability that both happen is the product of their individual probabilities. Flipping heads and rolling a six is one half times one sixth, which is one twelfth.

The probability that at least one of two events happens is different: you add the two probabilities and subtract the chance they both occur, so you do not double count the overlap. The calculator handles both the and case and the or case so you do not have to remember which formula to reach for.

Many probability questions really come down to counting how many ways something can happen. Permutations count arrangements where order matters, written as nPr, such as the number of ways to award gold, silver, and bronze among eight runners. Combinations count selections where order does not matter, written as nCr, such as choosing three pizza toppings from ten.

Both are built from factorials, but the combination formula divides out the orderings that a permutation would count separately. That is why nCr is always less than or equal to nPr for the same numbers. These exact counts underpin lottery odds, card hands, and countless real problems.

The tool runs entirely in your browser and covers single events, paired events, and exact counting in one place.

The biggest trap is treating dependent events as independent. Drawing two cards without replacing the first changes the totals for the second draw, so the simple multiplication rule no longer holds. Make sure the events really are independent before you multiply.

The other frequent mix-up is order. If swapping two items would count as a different result, you want a permutation; if not, you want a combination. Choosing the wrong one can inflate or deflate your count by a large factor, so pause on that question before you compute.