How to Multiply the Probabilities of Dependent Events

Two events are independent if the occurrence of one event does not affect the probability of occurrence of a second event; they are dependent if there is an effect. For example, if you flip a coin twice, the two flips are independent, because the effect of getting a head on the first toss does not affect the probability of getting a head on the second toss. However, if you draw two cards from a deck, without replacing them, then the events are dependent, because the probability of getting a heart on the second card changes based on whether the first card was a heart or not.

Instructions

    • 1

      Find the conditional probability of the second event, given the first event. For example, suppose you are drawing cards from a deck, without replacing them, and suppose an event is drawing a heart. Then you need to find the probability of getting a heart on the second card, given that you got one on the first. If the first card is a heart, then there are 51 cards left, of which 12 are hearts, so this is 12/51.

    • 2

      Find the probability of the first event. In the example, in a full deck, there are 13 hearts and 52 cards, so this is 13/52 = 1/4.

    • 3

      Multiply the two probabilities. For example, 1/4 * 12/51 = 12/204 = 3/51.

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