What are independent 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.

Events that do not affect one another whether they happen or not

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

Two events are said to be independent when the outcome of one event has no effect on the outcome of the other one. For example: If I say I'll come to your wedding when pigs fly; genetically engineering pigs to fly would still not ensure that I come to your wedding because my interest in your wedding is in no way related to the anatomy of a pig.

events A & B are independent if event A that has occurred doesn't affect the probability of event B from occurring

Independent events are those which do not affect each other. The probability of B happening is not affected by the outcome of A. For example... Rolling a dice twice. The two rolls are independent of each other, the second roll is not affected by the number you rolled previously.

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

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.

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!

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!

Independent events are events that don't depend on each other.

Here is an example of two independent events:

Suppose we take a coin and toss it twice.

Event A: getting a head the first time

Event B: getting a head the second time

If event A occurs (we get a head the first time), it doesn't tell us whether event B occurs or not (whether we get a head the second time or not). So event B is independent of event A.

Here is an example of two dependent events:

Suppose you have two balls, red and blue, in a bag. We pull out the balls one by one.

Event A: getting a red ball the first time

Event B: getting a red ball the second time

If event A occurs (the first ball is red) then event B doesn't occur (the second ball isn't red).

If event A doesn't occur (the first ball isn't red) then event B occurs (the second ball is red).

So event B depends on event A.

In probability, independent events are those whose occurrence or non-occurrence does not affect the probability of each other occurring. In other words, two events are independent if the probability of both events happening together is equal to their individual probabilities multiplied together.

For example, if you roll a die and flip a coin, the outcome of the die roll and the outcome of the coin flip are independent events because the result of one does not influence the result of the other. If you roll a die and get a 4, it does not change the probability of the coin landing on heads or tails.

Independent events are events where the outcome of one event does not affect the outcome of the other.

Independent events are events in probability theory where the occurrence of one event does not affect the probability of the other event occurring. In simpler terms, knowing that one event has happened gives no information about whether or not the other event will happen.

Mathematically, two events AA and BB are independent if:

P(A∩B)=P(A)×P(B)P(A \cap B) = P(A) \times P(B)

Where:

• P(A∩B)P(A \cap B) is the probability that both events AA and BB occur,
• P(A)P(A) and P(B)P(B) are the probabilities of events AA and BB, respectively.

For example:

• Rolling a die and flipping a coin are independent events because the outcome of the die roll does not influence the coin flip and vice versa.
• The probability of rolling a 6 on a die is 1/61/6, and the probability of flipping heads on a coin is 1/21/2. The combined probability of both happening is 1/6×1/2=1/121/6 \times 1/2 = 1/12.

When one event does not affect the outcome of the other event. Example Tossing a fair Coin and Rolling a fair die, one will not affect the other.