Difference between certain, random, and impossible events

An event represents a specific outcome or a set of potential outcomes from an experiment or situation.

The likelihood of an event occurring can range from 0% (impossible event) to 100% (certain event).

Based on this, events are generally classified into three main categories: certain events, random events, and impossible events.

  • Certain events
    A certain event is one that will definitely occur, meaning it has a 100% probability. These are scenarios where there is no doubt about the event taking place.

    For example, if a box contains only black balls, drawing a black ball from that box is a certain event.

  • Random events
    A random event is one that may or may not happen, and its outcome is not predetermined. The probability of a random event occurring lies somewhere between 0% and 100%, excluding both extremes. This means there is a chance the event could happen, but it’s not guaranteed.

    For example, drawing a black ball from a box that contains both black and white balls is a random event because it’s impossible to predict with certainty which ball will be drawn.

  • Impossible events
    An impossible event is one that will never occur, meaning it has a 0% probability. These are scenarios where it is certain that the event won’t happen.

    For example, if a box contains only black balls, drawing a white ball from that box is an impossible event.

The distinction between certain, random, and impossible events isn’t always objective. Often, it’s the context that determines whether an event is certain, random, or impossible.

For instance, in a lottery, a person would be guaranteed to win if they bought all the tickets, making the event certain. If they don’t buy any tickets, the event becomes impossible. If they buy one or more tickets but not all, the event remains random.

In summary, the difference between certain, random, and impossible events depends on their probability of occurring, which can be influenced by the context in which they are considered.

And so on.

 
 

Please feel free to point out any errors or typos, or share suggestions to improve these notes. English isn't my first language, so if you notice any mistakes, let me know, and I'll be sure to fix them.

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Calculating Probability