Difference Between Mutually Exclusive and Independent Events

Mutually Exclusive Events

Mutually exclusive events are events that cannot happen at the same time. For example, if you are flipping a coin, the two events are “heads” and “tails.” They are mutually exclusive because you cannot have both heads and tails at the same time.

Independent Events

Independent events are events that are not related to one another. For example, the outcome of one event does not affect the outcome of another. This means that the probability of both events happening is the product of the individual probabilities.

What are Mutually Exclusive Events?

Mutually exclusive events are events that cannot occur at the same time. For example, rolling a die and getting a 3 is mutually exclusive with rolling a die and getting a 5.

Examples of Mutually Exclusive Events:

A and B cannot both happen.

A or B can happen.

What are Independent Events?

Independent events are events that are not related to each other.

Formulas of Mutually Exclusive Events and Independent Events!

Formulas of mutually exclusive events:

P(A) = P(A ∩ B)
P(A ∪ B) = P(A) + P(B)

Formulas of independent events:

P(A) = P(A)
P(B) = P(B)
P(A ∩ B) = P(A)
P(A ∪ B) = P(A) + P(B)

Difference Between Mutually Exclusive and Independent Event:

Mutually exclusive events are events that cannot happen at the same time. Independent events are events that can happen at the same time.

Mutually Exclusive and Independent Events

Two events are said to be mutually exclusive if they cannot both happen at the same time. Two events are said to be independent if the occurrence or non-occurrence of one has no effect on the occurrence or non-occurrence of the other.

The events “rolling a 3 on a six-sided die” and “rolling a 5 on a six-sided die” are mutually exclusive. The event “rolling a 3 on a six-sided die” is independent of the event “rolling a 5 on a six-sided die.”

Mutually Exclusive vs Independent Events Examples

Mutually exclusive events are events that cannot happen at the same time. For example, two people cannot be in the same place at the same time. Independent events are events that can happen at the same time. For example, two people can be in the same place at the same time.

Difference Between Mutually Exclusive Event and Independent Event

There is a big difference between mutually exclusive events and independent events.

Mutually exclusive events are events that cannot happen at the same time. For example, flipping a coin and rolling a die are mutually exclusive events because you cannot flip a coin and roll a die at the same time.

Independent events are events that can happen at the same time. For example, flipping a coin and rolling a die are independent events because they are both random events and can happen independently of each other.

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