This is Stephanie from StatisticsHowTo.com,
and in this video I will show you about mutually exclusive events.
And I will show how to calculate probabilities for them
and to figure out if events are mutually exclusive or not.
I have got a venn diagram here of two events, A and B.
This could be any events like a could be buying a car,
B could be buying a house, and this area in the middle could be buying
a car and a house at the same time. So we have this thing called a union.
It is written like this. What this means is either A happens or B happens,
or they both happen at the same time. The formula for figuring out a union is going
to be. That is the probability of the union for A
and B is equal to probability of a plus the probability of B minus the probability of
the intersection of A and B. In other words you are looking for the probability
of this area, A happening plus the probability of B happening,
which is this entire area here, minus the center area here.
Mutually exclusive is when events cannot happen at the same time.
Let us say you only had enough money to buy a car or a house,
that means the center area, car and house, would not happen.
So the center area, this is 0, which means this last part of the equation here is 0.
In other words we can scratch this out. So if you have mutually exclusive events,
this becomes your probability equation. Now, it can be a bit confusing if you look
at a venn diagram like this so the preferable way is to draw it a little
differently. It makes more sense to draw a diagram like
this then you know you have the probability of A happening
and you have the probability of B happening but they cannot happen together.
So for mutually exclusive events we have the formula.
The probability of the union of A and B is equal to the probability of A plus the probability
of B, and you can only use this formula for mutually
exclusive events. So let us take a look an actual problem.
We have, if the probability of A is equal to 0.2 and the probability of B is equal 0.35.
But also given the probability of the union of A and B, that is equal to .51, are A and B
mutually exclusive? Well we know the formula for mutually exclusive
events is the union of probability of A and union B, right here 0.51.
Must be equal to the probability of A and the probability of B, so I am going to rewrite
that down here. Probability of A, the union of A and B, this
is 0.51. This must equal the probability of A, which
is given as .2 plus the probability of B and this is given as 0.35.
So is 0.51 equal to 0.2 plus 0.35? Well if I add these two together I get 0.55,
which is not equal to 0.51. So these are not mutually exclusive events.
If they were mutually exclusive then both sides of this equation would be equal.
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