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Transcript Probability

Probability
Statistics 2126
Introduction
• This stuff can be a bit hard, but don’t be
afraid
• We use probability for our purposes, so it
will be a tool, not an end in and of itself
• Why does this stuff matter to statistics
• Because we want to know about
populations, but we only have samples
example
• Say you flip a coin 10 times
• Say you get 10 heads, probably not a fair
coin
• Now it could happen, it could be fair
• But it is so unlikely we would probably
conclude that it is a fixed coin
• The only way to really know would be to
flip it an infinite number of times
A decision
• About 8 / 10 heads is roughly a 5 percent
probability of it being fair
• This is where we usually draw the line
• It also tends to fit with our intuitive feel
What is probability
• The total number of desired outcomes
divided by the total number of possible
outcomes
• It is just that simple
• So what is the probability of getting a red
card
• What is the probability of rolling a 4 on a 6
sided die?
A bit more complicated…
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2 dice
What is the probability of rolling a 7?
Well how many ways can you get a 7?
1,6 2,5 3,4 4,3 5,2 6,1
36 possible rolls
6/36 = 1/6 or .167
What about NOT rolling a 7?
properties
• 0 <= p <= 1
• A probability of 1 is all outcomes
• 0 is something that never happens
Spin (x)
Frequency (f)
1
2
2
5
3
3
4
9
5
1
Sooooo……
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
Probability Mass Function
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
However
• Most of the distributions that we look at
don’t have some shape that we can easily
find the area of
• Like say, a normal distribution
• How would we find the area under that?
• Well calculus
• Or a z table….
Well this must all have a point
• Using a z table
• Or this VERY cool website:
• http://davidmlane.com/hyperstat/z_table.ht
ml
• So if you know the z, you can find out what
the probability of getting a z score at a
certain level is.
So what is the probability of having
an IQ greater than 107?
x
z
107 100
z
15
z 7 / 15
z .47
p ( z .47) .3192