You’re at a magic show, and the magician walks up to you and asks you to chose a card. You pick a card and the magician claims to the audience, he’s sure you have picked an Ace. He dramatically reveals the card, and indeed its an Ace! So what did really happen here? Well, some magic has been performed, but also an event has occurred. Let’s learn more about probability and Events.
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What is an Event?
In probability, the set of outcomes from an experiment is known as an Event. So say for example you conduct an experiment by tossing a coin. The outcome of this experiment is the coin landing ‘heads’ or ‘tails’. These can be said to be the events connected with the experiment. So when the coin lands tails, an event can be said to have occurred.
You can download Probability Cheat Sheet by clicking on the download button below
Occurrence of an Event
In any given experiment or trial, there is a probability that either an event occurs or it does not. The probability of the occurrence of an event lies between 0 and 1.
The event E of a sample space S is said to have occurred if the outcome ω of the experiment is such that ω ∈ E. However if the outcome ω is such that, ω ∉ E we say that the event has not occurred.
Let us take the example of playing cards. Here the event E is drawing a face card. If you draw a king of spades, we say the event E has occurred. However, if you draw an eight of clubs, we say the event E has not occurred.
So if you look at the Venn Diagram, B is the Sample Set which defines all the probable outcomes of an experiment. Subset A is the Event Space, so an event will be said to have occurred if it falls into the subset.
Learn more about the Probability of Events here.
Types of Events
1. Simple Event
If the event E has only one sample point of a sample space, it is called a simple event or an Elementary Event. It is an event that consists of exactly one outcome. Let us understand this with an example. Say you throw a die, the possibility of 2 appearing on the die is a simple event and is given by E = {2}.
2. Compound Event
As opposed to a simple event, if there is more than one sample point on a sample space, such an event is called Compound Event. It involves combining two or more events together and finding the probability of such a combination of events.
For example, let us take another example. When we throw a die, the possibility of an even number appearing is a compound event, as there is more than one possibility, there are three possibilities i.e. E = {2,4,6}.
3. Certain Event
Just as the name suggests, an event which is sure to occur in any given experiment is a certain event. The probability of this type of event is 1.
4. Impossible Event
On the other hand, when an event cannot occur i.e. there is no chance of the event occurring it is said to be an impossible event. The probability of this event is 0. Like the probability that the card you drew from a deck is both red and black is an impossible event.
5. Equally likely Events
When the outcomes of an experiment are equally likely to happen, they are called equally likely events. Like during a coin toss you are equally likely to get heads or tails.
6. Complimentary Events
For an event E the non-occurrence of the event is called its complimentary event. Basically complimentary events are events that cannot occur at the same time. So when a die is thrown, getting an odd face and an even face are complementary events.
7. Mutually Exclusive Events
Two events are said to be mutually exclusive events when both cannot occur at the same time. Mutually exclusive events always have a different outcome. Two simple events are always mutually exclusive, whereas two compound events may or may not be.
If A and B are two events, then
( A ∩ B ) = Ø
P ( A ∩ B ) = 0
P ( A ∪ B) = P ( A ) + P ( B )
You can download Probability Cheat Sheet by clicking on the download button below
Solved Example for You
Q : Three coins are tossed simultaneously
P is the event of getting at least 2 heads
Q is the event of getting no heads
R is the event of getting heads on the second coin
Which of the pairs is mutually exclusive?
Sol : n (S) = 2 x 2 x 2 = 8
n (P) = HHT, HTH, THH, HHH = 4
n (Q) = TTT = 1
n (R) = THT, HHH, HHT, THH = 4
So Q & R and P & R are mutually exclusive as they have nothing in their intersection.
Question- What is an event in probability?
Answer- When we look at probability, we see that an event is a set of outcomes of an experiment to which there is an assigned probability.
Question- What are the different types of compound events?
Answer– The different types of compound events are two. One is mutually exclusive compound events and the other is mutually inclusive compound events. A mutually exclusive one is when two events cannot take place at the same time.
Question- What is a simple event probability?
Answer- Simple events are where an experiment takes place at a time which will create a single outcome. We make use of P(E) to denote the probability of simple events. Over here, E is the event and probability lies between 0 and 1. For instance, a coin toss.
Question- What is an event in probability example?
Answer- As we know the set of outcomes that we get from an experiment is an event. So an example would be when we toss a coin. The result of this means the coin can either land on the ‘heads’ side or ‘tails’.
