This is Stephanie from StatisticHowTo.com and in this video I'll show you how to tell
whether an event is independent or whether it's dependent.
Independent events are things that have basically nothing to do with each other.
An example would be driving to work and winning the lotto.
Your odds of winning lotto had nothing to do with driving to work and vice versa.
Driving to work has nothing to do with winning the lotto.
Though I guess you could argue, you won't drive to work anymore if you won the lotto.
A Dependent event, one event depends on the other.
For example your odds of getting a parking ticket depends on where you park.
If you park legally your odds of getting a parking ticket are practically zero.
If you park illegally then your odds of getting a parking ticket go up and they may go up
depending on where you park illegally. Let's take a look at some basic questions you
can ask to figure out whether your particular event is dependent or independent.
The first question you want to ask is, is it possible for the events to happen in any
order? I'll show you an example of a few events.
Here's three events that can clearly happen in any order.
Tossing a coin and rolling a die. You could roll the die first; it does not
affect the outcome of tossing a coin. Buying a car and then buying a coat.
You can buy the coat first or you can buy the car first.
And drawing cards from a deck. So if you are drawing five cards from a deck
with replacement that is you put the cards back.
You draw a king you put the king back; you draw an ace you put the ace back.
Those events could happen in any order. Events that can't happen in any order.
Parking and getting a parking ticket. Well you can't get a parking ticket without
parking first. So these two events must happen in a certain
order. Second example is surveying a group of people,
and finding out how many women are against gun rights.
We can't find out how many women are against gun rights, unless you do the survey first.
So these are two examples that must happen in order.
If your items must happen in order then they are Dependent.
If the events can happen in any particular order.
In other words it doesn't matter what order they appear in.
They might be independent they may be dependent. You have to ask yourself one more question.
That question is, does one event in any way affect the outcome of the other event?
Notice I said up here, when you're drawing cards from a deck, as long as you put each card back you have
1 out of 52 chance of pulling a card each time because there are 52 cards in a deck.
But let's say, you take two cards out of the deck. If you pull two cards you have 50 cards left
and if you pull another two cards you have 48 cards left.
Your probability of choosing any card that's left is going to go up.
the fewer cards you have, Like if you're down to 4 cards and you are choosing two, well
you've got a 50% chance of getting two cards. So if you are choosing with replacement, in
other words you are putting the cards back then you have an Independent event.
But if you don't put those cards back then you have a Dependent event.
This could go for bingo balls, rolling a certain number of dice.
As long as you start and finish with the same number of dice.
And when you repeat the process you have, say, 6 dice again that is Independent.
As far as purchasing a car and purchasing a coat.
Does one event in any way affect the outcome of the other event? Generally no.
But if you were to add something to this. And the only way you can get a coat was to
drive a car and the only way you could drive a car was by purchasing it, then these will
be Dependent events. But in most cases they would be independent.
So when you are deciding on dependent or independent just make sure you ask yourself these two
questions. This flow chart sums everything up if you
trying to decide whether an event is dependent or independent.
Start here, is it possible for the events to happen in any order, if the answer is no
it's dependent. If the answer is yes, you have to ask yourself
one more question, does one event in any way affect the outcome or the odds of the other
event. If your answer is no it's independent.
If your answer is yes its dependent. Check us out at StatisticsHowTo.com for more
examples and videos on everything Elementary Statistics.