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Those who study mathematics at a more advanced level will find that probability theory is an important topic to cover. For instance, the weather forecast for some regions indicates that there is a chance that it will rain today that is equal to or greater than fifty percent. A chance of something happening is what we mean when we talk about its probability. One or more outcomes are meant to be referred to when using the term “event.” The term “event” refers to the possible outcome of the situation. The term “total events” refers to any and all possible outcomes that may come about in connection with the experiment that was asked about in the question. Also referred to as favourable events, the events of interest fall under this category.
Sure and Unsure events
When the likelihood of an event occurring is one hundred percent, we refer to that occurrence as a sure event. There is a one in one chance of such a thing happening. One is very likely to obtain the desired outcome throughout the entirety of the sample experiment in the event of a certain event.
On the other hand, the probability of an event being zero is likely to be the case when there are no chances of that event occurring in the first place. It has been asserted that this occurrence cannot take place.
According to the nature of the events themselves, we can divide them into one of three categories, which are as follows:
- Independent Events
- Dependent Events
- Mutually exclusive events
First, let’s get a handle on the simple and the compound events so that we can have a better understanding of the dependent and independent events.
Simple Event
In the field of probability, a “simple event” is defined as an occurrence that only occupies a single point of the sample space.
The likelihood of an event taking place can be expressed as the ratio of the number of favourable outcomes to the total number of outcomes.
Compound events
A phenomenon is said to be a compound event if it can be represented by more than one sample point. The simple events are easier to understand than the compound events, which are slightly more complicated. The likelihood of these events occurring together involves the occurrence of more than one event at the same time. The sum of all the possible outcomes of a compound event is 1, which is the same as its total probability.
The equation shown here is the one that is used to compute probabilities:
To begin, we will calculate the likelihood that each event will take place. After that, we will add all of these probabilities together and multiply the total. If there is more than one event taking place, then the numerator, which represents the number of positive outcomes, will be greater than 1.
Dependent Events
Events are said to be dependent on one another when their outcomes are determined by the results of events that have already taken place in the past. In other words, two or more events that are dependent on one another are referred to collectively as dependent events. If by some fluke one event is altered, then another is probably going to turn out differently.
Accordingly, if the occurrence of one event does influence the likelihood that the other event will also take place, then the two events are said to be dependent on one another.
Independent events
Events are considered to be independent if their occurrence does not depend in any way on the occurrence of any other event. It is said that two events A and B are considered to be independent if the probability of one event A occurring does not change depending on the likelihood of another event B occurring.
Examples:
A toss of the coin.
Sample Space S equals “H, T” in this case, and both “H” and “T” are considered to be independent events.
Rolling a die.
All of the events that make up Sample Space S = 1, 2, 3, 4, 5, and 6 can be considered independent.
Both of the aforementioned examples are straightforward occurrences. Even compound events can be independent events. Take, for instance:
The game consists of rolling a die and flipping a coin.
Sample space is denoted by the equation S ={(1,H), (2,H), (3,H), (4,H), (5,H), and (6,H), (1,T), (2,T), (3,T), (4,T), (5,T),(6,T)}
These occurrences cannot take place simultaneously, so we can say that they are independent of one another.
Mutually Exclusive Events
It is said that two events, A and B, are mutually exclusive events if it is impossible for both of them to take place at the same time. Events that are mutually exclusive will never have a result that is the same.
Conclusion
When the likelihood of an event occurring is one hundred percent, we refer to that occurrence as a sure event. There is a one in one chance of such a thing happening. One is very likely to obtain the desired outcome throughout the entirety of the sample experiment in the event of a certain event.In the field of probability, a “simple event” is defined as an occurrence that only occupies a single point of the sample space.A phenomenon is said to be a compound event if it can be represented by more than one sample point.Events are said to be dependent on one another when their outcomes are determined by the results of events that have already taken place in the past.Events are considered to be independent if their occurrence does not depend in any way on the occurrence of any other event.
