Dependent vs Independent events


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.

1 thought on “Dependent vs Independent events

  • Hmmm. Alice decides to buy an ice cream in Australia. Bob decides to go skiing in Canada. These can happen in any order, and Alice's decision does not effect the outcome of Bob's decision or vice versa (in fact, if they make the decision at almost the same time, then no information can travel between them, as it's fundamentally fixed by the speed of light . Yet they ARE dependent. Alice's decision to buy an ice cream is more likely to be made in Australian summer, in which case it's more likely to be winter in Canada, in which case Bob is more likely to go skiing. The problem is that dependence does not mean causation – only correlation. Statement 2) implies causation. Alice cannot change the seasons by buying an ice cream, and thus can't affect Bob's choice of going skiing in Canada. So A cannot cause B, or B cause A. Two events may be correlated without causation. So a third question must be asked. Does there exist another event which can affect the two events considered?

Leave a Reply

Your email address will not be published. Required fields are marked *