One of the topics covered under Data Analytics is mutually exclusive and independent events which is a major aspect of probability. This topic gave me insight into some of the terms and events that normally I do not understand their meaning or relevance. Previously, when I hear tossing a coin and getting head or tail, I normally thought it only applies to referrers in football games using the process to ascertain the team that will start the match first. It usually sounds Greek to me but now I know better. Going through the Data Analytics course has helped me appreciate some of the concepts and meanings involved.
Let us work through mutually exclusive and Independence events as a topic in the Data Analytics course.
What are mutually exclusive events?
Mutually exclusive events are those events that cannot happen simultaneously. Two events are mutually exclusive when they cannot occur at the same time. For example, if we flip a coin, it can only show a head or a tail, not both. We cannot get both heads and tails at the same time. The two events do not have joint occurrences. One happening means the other did not happen. i.e., A and B did not happen together. If you are computing the two unions, you simply sum up their probability P(A)+P(B). You do not have to subtract their interception because the two do not happen together.
Example of Mutually Exclusive Events:
There are 52 cards in a deck. Out of these cards, we have 4 kings and 4 queens.
- the probability of getting a King = 1/13, so we can say P(King)=1/13
- the probability of getting a Queen is = 1/13, so we can say P(Queen)=1/13
When we combine those two Events, we cannot get queen and king at the same time thus,
P (A and B) = 0
Therefore, we can say the probability of a King, or a Queen is (1/13) + (1/13) = 2/13
What are independent events?
Independent events are those whose occurrence does not affect the occurrence of the others. Events A and B are said to be independent if the chances of B occurring are not affected by the happening of event A. For example, if we flip a coin in the air and get the outcome as Head, then again if we flip the coin but this time, we get the outcome as Tail. In both cases, the occurrence of both events is independent of each other. One does not influence the occurrence of the other. Such events can be computed by dividing their interception by their prime or joint over prime.
P(A|B) = P(A)
P(B|A) = P(B)
P (AnB) = P(A)P(B)
For simplicity, let us use the below table to differentiate between the two:
|Comparison on the Basis of||Mutually Exclusive Event||Independent Event|
|Definition||Here the events cannot happen simultaneously||The occurrence and outcome of one event don’t affect the occurrence and outcome of the other event|
|Dependency||Occurrence of event A results in non-occurrence of event B||The occurrence of event A does not affect event B in any manner|
|Occurrence of both events||The mathematical formula for the representation of the mutually exclusive event is P(AnB)=0||The mathematical formula for the representation of the Independent event is P(AnB)=P(A).P(B)|
Therefore, mutually exclusive events are not independent, and independent events cannot be mutually exclusive.