Types of Events in robability

Probability is a very important branch of mathematics. Understanding probability can make mathematical calculation easy. The probability of an event is the number of favorable outcomes to the total number of outcomes. P(E)= no.of favourable outcomes/ total number of outcomes.

The collection of some or all possible outcomes of a random experiment is known as an event. In probability, there are many different sorts of events. Each particular event has its own set of characteristics. Basically, we can say that when we do some experiment there must be a possibility of some outcomes to occur; this outcome is known as an event. 

A sample space is defined as the collection of all possible outcomes of an experiment, and an event is one of those possible outcomes; similarly, an experiment might have several events (outcomes). As a result, an event can be defined as a subset of Sample Space.

What is an event in probability? 

Suppose we toss two coins. Then the total number of outcomes will be the sample space which is given by {HH,TT,HT,TH} . let an event (E) be defined as getting at least 1 tail. Then, it is given by E={TT,HT,TH}. Thus, we can conclude that event E is the outcome of a tossing coin and a subset of sample space.

Types of events in probability 

There are different types of events in probability. For a random experiment, there can only be one sample space, but there can be many different sorts of events. Some events are given below- 

• Independent events – as the name suggests independent events are events that do not depend on the previous outcomes. Or we can say that they have no connection with any other event. The probability of an event will be the same no matter how many times it has been done. 

For example – if we roll two dice simultaneously the result on the first one is independent of the result of the other. 

If A and B are two independent events, then 

P(A and B) =P(A)*P(B).

• Dependent events – dependent events are those events whose outcome depends on the previous one. The probability of occurrence will be affected by previous events.

For example – suppose a bag contains a number of colored balls. A ball is chosen randomly from it. Each time you take a ball the chances of drawing out a certain color will change.

If A and B are two dependent events,

P(B and A) = P(A)* P (B after A).

P(A)- the probability of event A.

P(B after A) – the probability of event B.

1. Simple event- simple events are that event that has a single result from the total number of outcomes. For example- the probability of getting the number 9 from ten cards- 1,2,3……,10. So, E= {9}.
2. Compound events- compound events have more than one result. For example- getting an even number by rolling a die. E={2,4,6}.
3. Sure event- events which are surely going to happen are known as sure events. For example while tossing a coin the probability of getting head is a sure event.
4. Impossible events- impossible events are those having the possibility of occurrence equal to zero. For example, the probability of drawing a blue ball out of red and green balls is an impossible event.

Conclusion 

P(E)=number of favourable outcomestotal number of outcomes

Event is the collection of all possible outcomes. We have different kinds of events namely- independent event, dependent event, simple event, compound event, sure event, impossible event. An event is one of the possible outcomes of an experiment, and a sample space is the collection of all possible outcomes of an experiment; similarly, an experiment may have numerous events (outcomes). As a result, a subset of Sample Space can be defined as an event.