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Probability is
defined as the measure of the
"likelihood" of an event, or
outcome.
Another way of saying that is,
"What is the chance of
something happening?"
Probability is all about the
certainty, the
uncertainty, and the
prediction of something happening.
Some events are impossible,
other events are certain to occur,
while many are possible, but
not certain to occur.
Let's look at a few examples of each of these:
Impossible Events:
Moving Mt.
Everest to New York State
The sun turning to ice
Oscar the Grouch becoming President of the U.S.
Rolling a 7 on a single die
Finding the color purple on the American flag.
Certain Events:
Rolling a
1,2,3,4,5,or 6 on a single die
Today will be 24 hours long
The number 10 is less than the number 11
George Washington was the first U.S. President
Flipping a coin and getting either a head or a tail
Possible, But Not Certain Events:
Picking the King
of Hearts from a deck of cards
Landing on "Boardwalk" in Monopoly
Rolling a 3 on a single die
Getting a "100" on a Math test
Flipping a coin and getting a "head"
Now let's look at how we determine the
Probability
of something happening
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The probability of an
event is the chance that it will occur, expressed as a ratio of
a specific event to all possible events.
Or....
Probability =
number of actual events
number of possible events
Or....
Probability = number of favorable outcomes
number of possible outcomes
The probability of an event that is
certain to occur is 1.
The probability of an event that is
impossible to occur is 0.
The probability of an event that is
possible is >0 and <1
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Before
we go any further let's look at a few simple examples of these
rules...
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Let's try a
few...
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For this experiment
we have a bag containing 10 cards. Each card is
numbered differently from 1 - 10. In each trial we
will reach into the bag and pull out exactly 1 card, look at
it, and then return it to the bag.
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1. What is the probability of
choosing a "7"?
Let's see, there is only 1 favorable outcome,
because there is only 1 - "7" in the bag. There are a
total of 10 possible outcomes because we could
have selected any of the 10 cards.
Therefore the probability of choosing the "7" is:
P(7) = 1
10
2. What is the probability of
choosing an
even numbered card?
In the bag there are 5 even numbered cards:
2,4,6,8,and 10.
That means there are 5 favorable outcomes out of the
10 possible outcomes.
Therefore the probability of choosing an even card is:
P(Even) = 5
10
OR...1/2 !
3. What is
the probability of choosing a
card numbered 1 -10?
I think the chances
must be pretty good...don't you?
After all, there are 10 cards in the bag, and each card is
numbered differently from 1 - 10
Therefore the probability of choosing a card numbered 1-10:
P(1-10) = 10
10
OR...1 !
4.
What is the probability of choosing a "12"?
In the bag there are
no cards with the number "12" on it. Therefore the
number of favorable outcomes is 0.
So, the probability of choosing a "12" is"
P(12) = 0
10
OR...0 !
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Before we go to the
practice page for this lesson, there is one more very
important fact to know about probability.
The sum of the probability of
an event happening and the probability of an event not
happening is ALWAYS 1!
Let's look at an example:
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In this experiment we will
simply roll a single die one time, record the result, and roll the
die again.
What is the probability of rolling a "3"?
Since a die has 6 faces, but only one of them a "3"
P(3) = 1
6
Now, what is the probability of NOT rolling a "3"?
Since there are 5 other possible outcomes
P(not3) = 5
6
Do you see that if you add the probability of rolling the "3" to the
probability of NOT rolling the "3" that the sum is 1
1/6 + 5/6 = 1!
That means that if you know the probability of something happening,
to determine the probability of it NOT happening, simply subtract
the favorable probability from 1.
If the probability of it raining today is 2/5, the probability of it
NOT raining is 1 - 2/5 = 3/5!
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We have looked at a
lot of material on this page, and there is still a lot to learn about,
but I think it is a good idea to try a few of these on your own before
we go any further.
So, for
some practice on your own....
Click here!
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