Independence and Incompatibility of Random EventsIndependence and Incompatibility of Random Events

In probability theory, independence and incompatibility are concepts related to the relationship between random events.

  1. Independence: Two events are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the occurrence or non-occurrence of the other event. In other words, knowing whether one event happens provides no information about the likelihood of the other event happening.
    Events A and B are independent if P(A intersection B) = P(A)*P(B).
  2. Incompatibility: Two events are incompatible if they cannot occur simultaneously. If the occurrence of one event excludes the possibility of the other event happening, they are considered incompatible. For example, flipping a coin and getting heads and tails simultaneously is incompatible since the coin can only show one side at a time.
    Events A and B are incompatible if P(A intersection B) = 0.

Examples of independent and incompatible events:

Independant eventsIncompatible events
Results of flipping a fair coin and rolling a fair dieRolling a die and getting an odd number and an even number on the same roll
Results of flipping two different coinsSelecting a card from a deck and getting a red card and a black card at the same time


You draw a card from a standard deck with replacement (after we have drawn a card, we return it back to the deck) . What is the probability of drawing a red card (heart or diamond) followed by drawing a black card (spade or club)?

Select the correct answer

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Section 1. Chapter 5