How to Calculate Joint Probability

Looking for the upper hand in a card game? Or maybe the scientific possibility of an event occurring? Find the probability of multiple events occurring together using multiplication.


  • Step 1: Determine any additional probabilities of events and write them down.
  • Step 2: Take the product of all the fractions to find the joint probability and bask in the fact that you now know the odds.
  • FACT: The modern theory of probability was created in 1645 by Blaise Pascal and Pierre de Fermat, French mathematicians trying to answer a question about the odds of a dice game.
  • TIP: Using the example, the Jack was kept out of the deck. The probability of choosing a Queen from the same deck is now four out of 51.
  • Step 3: Determine the probability of the next event with or without replacement.
  • TIP: For example, the probability of choosing a Jack from a full deck of cards is four out of 52.
  • Step 4: Decide if the next event is based on replacement. For example, choosing a Jack and keeping it in your hand or placing it back in the deck.
  • Step 5: Determine the probability of the first event and write it as a fraction.

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