What are independent events?

 one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)

Hi Noel,

Independent events are events which are not affected by previous events. For example, if a fair coin is flipped, the coin "has no idea" that whether it landed on tails or heads before, and so each toss is independent. Hopefully that helps.

In probability theory, independent events are events that have no influence on each other. Specifically, the occurrence of one event does not affect the probability of the other event occurring.

More formally, two events A and B are independent if and only if the probability of both events occurring is equal to the product of the probabilities of each event occurring independently. That is:

P(A and B) = P(A) x P(B)

For example, the probability of it raining today is 40% (0.4) and the probability of me having rice and chicken for lunch is 50% (0.5). These two events do not depend on each other. The probability that I eat rice and chicken does not depend on the probability of it raining. Hence, these two events are deemed independent.

Independent events are events where the probability of an event happening is not dependent on the outcome of another event.

For example, if you flip an unbiased coin (so probability of getting heads is 1/2 and so is the probability of getting tails) twice in a row, the probability of getting heads on the second flip is 1/2 - the first flip does not affect this, a coin has no memory! :)

One thing to note though is that an exam question could show pretty much the same scenario but the events could be either dependent or independent.

Let's look at an example: John is taking two tests next week - first one in Biology and the second one in Chemistry. The probability that John passes the Biology test is 0.8. There are two options:

1) If John passes the Biology test, the probability he passes the Chemistry test is 0.75.

But if John doesn't pass the Biology test, the probability he passes the Chemistry test is only 0.6 as he has lost some confidence.

Here the events of John passing the Biology test and him passing the Chemistry test are dependent because the probability of passing the Chemistry test depends on whether he has passed the Biology test or not.

2) John's spirit is not affected by whether he has passed the Biology test and the probability that he passes the Chemistry test is 0.75, no matter what happened with the Biology test.

Here the events of John passing the Biology test and him passing the Chemistry test are independent because the probability of passing the Chemistry test does not depend on whether he has passed the Biology test or not, it is 0.75 in both cases.

You don't have to worry about trying to decipher which scenario it could be in an exam question - it can be easily identified from the information they give you.

If there is any sentence such as "If John passes the Biology test, the probability he passes the Chemistry test is ...", then we have dependent events.

If they give you only the information that the probability he passes the Biology test is e.g. 0.8 and the probability he passes the Chemistry test is e.g. 0.75, then the probability of passing the Chemistry test is 0.75, no matter the result ot the Biology test.

In some questions, you are asked to show two events are independent - but that would be a whole another question! :)

Hope all makes sense but if some part is even a little bit unclear, please do let me know!

Events are "things" that are happening at a particular time. Let us call two such events, event A and event B. We would say that events A and B are independent IF they have nothing in common with each others and no not alter possible OUTCOMES of an experiment. For example, let event A be the probability of getting a head H on a fair, two sided coin. Let event B be rolling the number 6 on a fair, 6-sided coin. Let us say that we toss the coin and then roll the die and record our result. The probability of getting a Head on the coin has nothing to do with the probability of getting a 6 on the die; so these two events are independent. Can you think of another example of an independent event? Can you think of two events which are dependent?

Independent events are those events whose occurrence is not dependent on any other event. Think of a coin. If you flip a coin in the air you can either get the outcome of Head or Tail. Assume that, after the first flip you get the outcome of Head. If you flip it again for the second time, you will independently of the first flip have equal probability of getting an outcome of Head or Tail.

Independent events are events that are not affected for previous events.

Hi Noel. Think of whether the first event might effect the second. If yes, then they are dependent. If not, they are independent. For example, throwing a coin. If I throw it once (the first event) and then again (the second event) will what happened to the coin the first time have any effect on the second time? The answer would be no, so the two throws are independent, so the two events are independent.

Independent Events are not affected by previous events.

For Example,

A coin does not "know" it came up heads before. 

And each toss of a coin is a perfect isolated thing.

You toss a coin and it comes up "Heads" three times ... what is the chance that the next toss will also be a "Head"?

The chance is simply ½ (or 0.5) just like ANY toss of the coin.

What it did in the past will not affect the current toss!

Two or more events are independent if the outcome of one of them does not affect the probability that any of the others will occur.

For example, consider the following two events: Tossing a coin and rolling a die.

The outcome of tossing a coin is either heads or tails. The outcome of rolling a die is a number from 1 to 6.

Assuming we have a fair coin and a fair die, the probability of getting heads is 1/2 and the probability of rolling a 3 is 1/6.

These two events are independent because whether or not I get heads, this does not alter the probability of rolling a 3 - the probability of rolling a 3 is still 1/6 even if I get tails.

An independent event is an event that does not affect the other events' probability for example the price of a phone and the colour of the phone are independent events

In simple terms, independent events are events that do not affect each other, so the probability of each of them happening does not depend on whether another event happens (or doesn't happen).

Hi Noel, an independent event in probability is an event that doesn't rely upon, or have any reliance on another event. Such as: we know that each role of a dice is random, and you could in theory roll 10 5s in a row, because the outcome of the previous roll does not effect the next roll.

This event however has a 1/6 probability of hitting that 5 each time, and doesn't change due to previous outcomes.

On the other hand, a dependant event is one that is affected by something else, for example, if I had a bag of 4 sweets. 1 red, 1 yellow and 2 blue. If I asked student 1 to choose a sweet form the bag and he chooses blue, the probability of student 2 choosing blue has reduced. Student 1 had a 1/2 probability of choosing blue, whereas student 2 only has 1/3 chance.

Hope this clarifies the difference for you

In probability, two events are independent if the incidence of one event does not affect the probability of the other event. If the incidence of one event does affect the probability of the other event, then the events are dependent.

independant events are where the probability of one event does that influence the probability of the other happening.