What are independent events?

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.

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

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.

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.

Two events are said to be independent if the outcome of one does not effect the probability of the other.

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).

Independent events are events that are not dependent on the outcome of any previous event. For example, if we flip a coin and get heads initially and then flip it again, but this time, we get tails. The outcome in both cases are independent of each other. It is not because we got heads the first time, we got tails for the second flip. They are not dependent on each other.

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.

Hi there,

It is an event that is not affected by other events.

they are totally separate.

i hope this helps

Two events, E & F are independent if the occurrence of E does not affect the probability of event F.

Event B is independent of Event A if the probability of Event B doesn't depend on whether event A has happened or not.

That sounds a bit confusing but let me take you through an example to help.

Say you have a bag of 20 marbles. In this bag there are 10 green marbles, 7 red marble and 3 yellow marbles.

Say you pick a marble from the bag. The probability of of you picking a green marble from the bag is 1/2 (10/20), the probability of picking a red marble is 7/20 and a yellow marble 3/20.

You then decide to pick another marble, and you put the marble you've just picked back into the bag.

The probability of choosing a marble of each colour remains the same. In this case Event B is the second marble chosen, and Event A is the first marble chosen. Event B's probability does not change/depend on Event A, therefore it is INDEPENDENT.

However if you were not to put the marble back once you had chosen it, the probability of choosing a marble of each colour would change.

Let's try the same example again. Let's say the first marble you choose is red. You keep it out of the bag and choose another. The probability of choosing each colour has now changed because you have one less marble, and the number of red marbles in the bag has decreased by one because one red marble is outside the bag.

So now the probabilities are as follows

Green - 3/19

Red - 6/19

Yellow - 3/19

Again in this case Event B is the second marble chosen, and Event A is the first marble chosen. But in this case Event B's probability DOES change/depend on Event A, therefore it is DEPENDENT.

Hope that helps :)

Independent events are events that are statistically independent. This means that the outcome of one event does not affect the outcome of another.

Mathematically, the probability of two independent events occurring, P(A and B), is found by multiplying the Probability of one P(A), by the other P(B)

Independent event P(A and B) = P( A) * P(B).

An example of this would be if a dice is rolled twice, the outcome of the first roll does not affect the outcome of the second. In this scenario, the chance of rolling any number between 1 and 6 on a 6 sided die is 1/6 on each roll.

Events that are not independent are dependent events, with these, the outcome of one event does affect the outcome of another.

An example of this might be what someone wears and the weather that day. If it is raining the chances of wearing a rain jacket are increased, therefore these are the clothing choice is dependent on the weather.

Independent events occur when the probability one event occurring has no effect on the probability of the second event occurring eg flipping a coin