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Two events such that the happening of one event prevents the happening of another event are referred to as mutually exclusive events. In other words, two events are said to be mutually exclusive events if they cannot occur at the same time.
Example: Tossing a coin can result in either heads or tails, but both cannot be seen at the same time.
The event that cannot happen is called an impossible event. An event that is not a part of the experiment or which does not belong to the sample space of the outcomes of the experiment can be referred to as an impossible event. The probability of an impossible event is zero (0)(0)
Example: Probability of getting number 88 on throwing a single dice.
Complementary events occur when there are just two events, and one event is exactly opposite to the other event. Hence, A∪A¯=setofsamplespaceA∪A¯=setofsamplespace
For an event with probability P(A)P(A), its complement is P(A¯)P(A¯) such that
P(A¯)+P(A)=1P(A¯)+P(A)=1
Example: In an examination, the event of success and the event of failure are complementary events.
P(Success)+P(Failure)=1
In probability, an event is an outcome or defined collection of outcomes of a random experiment. Since the collection of all possible outcomes to a random experiment is called the sample space, so another definition of an event is that it is any subset of a sample space. The likelihood of occurrence of an event is called probability.
There are many events associated with the sample space. Some of the important events are listed below:
When the events have the same probability of happening, then they are called equally likely events. The results of a sample space are called equally likely if all of them have the same probability of occurring.
The following are some examples of likely outcomes:
In axiomatic probability, a set of rules or axioms are set, which applies to all types. In this probability, the chances of occurrence and non-occurrence of the events can be quantified. It is the likelihood of an event or outcome occurring based on the occurrence of a previous event or outcome.
Experimental probability is a probability that is determined based on a series of experiments. Therefore, it is based on the data which is obtained after an experiment is carried out. It is the ratio of the number of times an event occurs to the total number of experiments that are conducted.
Theoretical probability is based on the possible chances of something happening. It is based on what is expected to happen in an experiment without conducting it. It is the ratio of the number of favorable outcomes to the total number of outcomes.
There are mainly 33 types of probabilities: