Difference Between Mutually Exclusive And Independent Events : In statistics and probability, knowing the concepts of independent and mutually exclusive events is essential. The relationships between events in a probability experiment are explained by these concepts. A complete discussion on the difference between mutually exclusive and independent events will be discussed below.
The difference between mutually exclusive and independent events is that a mutually exclusive event happens when two events cannot occur simultaneously, but an independent event occurs when one event is unaffected by the presence of the other event. A mutually exclusive event is one in which a coin is thrown, and one of two outcomes is possible: head or tail. As a result, both of these occurrences are mutually exclusive. However, if we flip two distinct coins, the probability of a Head or Tail on one is independent of the other. Before we discuss the difference between mutually exclusive and independent events, let’s first understand their meaning. Achieve JEE excellence with PW JEE Online Course . Join now to fulfill your engineering dreams!Difference Between Mutually Exclusive and Independent Events | ||
Points | Mutually Exclusive Events | Independent Events |
1 | Events that cannot happen at the same time or overlap | Events that do not influence each other |
2 | If one event occurs, the other cannot happen | The probability of one event does not affect the other |
3 | No common outcomes or elements between events | Events can share outcomes or elements |
4 | Combined probability is the sum of individual probabilities | The probability of one event is not influenced by the other |
5 | Joint probability is zero for mutually exclusive events | Joint probability is the product of individual probabilities for independent events |
6 | Probability calculation involves adding individual probabilities | Probability calculation involves multiplying individual probabilities |
7 | Zero probability of occurring together | Non-zero probability of occurring together |
8 | Venn diagram sets do not overlap for mutually exclusive events | Venn diagram sets may overlap for independent events |
9 | Presence or absence of one event provides no information about the other | Presence or absence of one event does not give information about the other |
10 | Examples include flipping a coin and getting heads or tails, rolling a dice, and getting an odd or even number | Examples include flipping a coin and rolling a die, drawing cards with replacements from a deck. |