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.

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

we look at events when dealing with probability or the chances of something happening.

Now to answer your question (and to give the answer as part of a bigger picture):

An independent event has no connection to and therefore does not affect the chances of another event happening.

For example being a dog owner and winning the lottery (neither event will have a direct impact on the other)

More mathematically - think of dice, if you roll a fair 6 sided dice and record the score and then roll that fair 6 sided dice again and record it score once more, the two scores are completely separate events and neither has an impact on the chances of the other happening.

Now, for the wider picture, we also have dependant event and these are the opposite of independent events. That is a dependent event is directly affected by another event (in other words a dependent event relies on another event happening first)

For example buying 100 lottery tickets and winning the lottery (those ten tickets could be the one that wins the lottery and therefore these ten tickets increase your chances of winning the lottery (whereas above, owning a dog does not!)

Finally, more mathematically, if you have a standard pack of playing cards containing the 52 scoring cards from Ace up to King in all four suits (heart, diamond, spade, club). Imagine taking a card out (for example 7 of hearts, this has a probability of 1/52), now you have already taken this card out - if you take another card from the deck (5 of clubs) its probability will be 1/51. the reason for this is you have already removed the 7 of hearts from the deck and there are now no longer 52 cards left, there are now 51 cards left and hence only 51 possibilities to choose from.

I hope this helps!

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

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.

Let A and B represent two events

Then we can say that A and B are independent if P(A ∩ B) = P(A)*P(B)

So in all knowing the probability of one event i=eg - A doesn't change the probability of B

independent events are mutually exclusive events, the occurrence of event A is not dependent (does not affect) the occurrence of event B

An event that does not depend on anything