anigeo said:what is the basic difference between mutual exclusiveness and independence?
actually i got this as a difference between fundamental principle of addition and fundamental principle of multiplication.
Mutual exclusiveness refers to two events that cannot occur at the same time. Independence refers to two events that have no influence on each other.
Mutual exclusiveness and independence are different in that mutual exclusiveness means the occurrence of one event prevents the other from happening, while independence means the occurrence of one event has no effect on the likelihood of the other event happening.
An example of mutual exclusiveness is flipping a coin and getting either heads or tails. An example of independence is rolling a die and flipping a coin, as the outcome of one event does not affect the outcome of the other.
Understanding the difference between mutual exclusiveness and independence is important in statistics and probability as it affects the calculations and interpretations of data. The wrong assumption of mutual exclusiveness or independence can lead to incorrect conclusions.
No, two events cannot be both mutually exclusive and independent. If two events are mutually exclusive, they cannot occur at the same time, which means they are dependent. If two events are independent, they can occur at the same time, which means they are not mutually exclusive.