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Two events a and b are independent if the knowledge that one occurred does not affect the chance the other occurs. These concepts are all very tricky but upon learning by example these probability concepts are actually very simple.

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If two events a and b independent then p a b p a p b.

Independent vs mutually exclusive. It can t be both. Clearly the roll of a die must result in a number that is either odd or even. For example the outcomes of two roles of a fair die are independent events.

P a b p a p b for example when choosing a ball at random from a bag containing 3 blue balls. Mutually exclusive events are represented mathematically as p a and b 0 while independent events are represented as p a and b p a p b. Mutually exclusive vs independent events in mathematics the probability between two events bears some characteristics like mutuality exclusivity and dependency.

Independence of events means happening of a does not affect the happening of b. If two events a and b mutually exclusive then p a b 0. Two events are independent if the following are true.

Difference between mutually exclusive and independent events mutual exclusivity of events means there is no overlap between the sets a and b. In a venn diagram the sets do not overlap each other in the case of mutually exclusive events while if we talk about independent events the sets overlap. Is the mathematical symbol for union.

B the roll of a die is even. P a and b p a p b. A the roll of a die is odd.

For two mutually exclusive events a and b the probability of either one occuring p a b is the sum of the probability of both events. Independent and mutually exclusive do not mean the same thing. Two events are said to be mutually exclusive if they can t both happen at the same time.

Here are two events that are mutually exclusive.