Work out the chance of an event from counts, or combine two events and see the odds each way.
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This probability calculator answers two kinds of question. Give it counts, such as successful outcomes out of all outcomes, and it returns the chance, the chance of the opposite, and simplified odds. Or enter the chances of two events and see how they combine when they happen together.
Independent events do not change each other. A coin flip lands the same way no matter what the last flip did, so chances can be multiplied to find the odds of both happening.
Mutually exclusive events cannot happen at the same time. A single die roll cannot land on both 3 and 5, so the both happen line reads zero and the chances simply add for at least one.
The unit switch matters more than it looks. A chance typed as 50 means one thing as a percent and something wildly different as a decimal, so the tool makes you pick the unit with the switch rather than guessing what you meant.
The four combined lines cover the questions people actually bring. Both happening is the jackpot case, at least one is the safety case, exactly one covers either-or outcomes, and neither is the miss case that plans around failure.
Multiplying two chances is only right when the events are independent. When one event changes the odds of the other, plain multiplication overstates or understates the answer.
Cards show it well. Drawing two aces from a deck without putting the first one back works out as 4/52 x 3/51, about 0.45 percent, because only three aces remain for the second draw. Plain multiplication gives about 0.59 percent, which is wrong for that draw.
Count based probability also assumes every outcome is equally likely. That holds for a fair die or a well shuffled deck, and falls apart for loaded dice or a spinner that favors one side.
The single event mode rests on the same fair play assumption. Counts only turn into chances when every outcome really can land, which is why the tool shows the opposite chance and the simplified odds alongside the main figure.
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Divide the successful outcomes by all outcomes. Rolling a 6 on a fair die is 1 successful outcome out of 6, and the tool turns that into a percentage and simplified odds of 1 in 6.
It means one event does not change the chance of the other. Coin flips and die rolls are independent. Drawing cards without replacing them is not, because the deck changes after each draw.
It means the two events cannot both happen. A single die roll cannot land on 3 and on 5 at the same time, so for that roll the chance of both is zero.
Because the second draw depends on the first. After one ace leaves the deck, 3 aces remain among 51 cards, so the true figure is 4/52 x 3/51. The 0.59 percent figure comes from multiplying as if the deck never changed.
Either works, as long as the switch matches what you typed. 50 as a percent and 0.5 as a decimal describe the same chance, and the switch is never guessed for you.
They restate the chance as a small whole number ratio, the way bookmakers and board games quote it. A 1 in 6 chance is the same fact as about 16.7 percent, in a form some people read faster.
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