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Probability part 1

posted Oct 28, 2010, 3:16 PM by Prof Kiernan   [ updated Oct 28, 2010, 3:56 PM ]
So it seems that most people are having an issue with regular probabilities using a table so here's how I'd do a problem with a table of values
I went around campus and asked people who had laptops: if they had a MAC or PC, and if they owned an iPad/iPod/iPhone and got the following values:

 MAC computer
PC
computer
Total
 iPad 5 27
 iPod 64
 10
 iPhone 3 10 13
 Total 14 16 30

All I need to do to find any basic probability is figure out what I'm talking about then divide it by a total. The trick is figuring out what that total is supposed to be.

Any time I have a single word inside the probability i will most likely use the total of the whole group as the denominator (bottom of the fraction). For example:

If I wanted to find the probability of having a MAC computer I'd get the following:
P(MAC) = the number of MAC users/ the overall total = 14/30
If I wanted to find the probability of having a PC computer I'd get the following:
P(PC) = the number of PC users/ the overall total =16/30
If I wanted to find the probability of having an iPad I'd get the following:
P(iPad) = the number of iPad users/ the overall total= 7/30
If I wanted to find the probability of having an iPod I'd get the following:
P(iPod) = the number of iPod users/ the overall total= 10/30
If I wanted to find the probability of having an iPhone I'd get the following:
P(iPhone) = the number of iPhone users/ the overall total= 13/30

Now If I wanted to find the probability of owning an iPod or a PC I'd use a different set of rules. Then you've got to figure out what this formula means P(A or B)=P(A)+P(B)-P(A and B) ...The formula is basically saying that since I am saying one OR the other I can add the probabilities together and make sure I don't count things twice!

If I wanted to find the probability of owning an iPod or a PC I'd do the following:
P(iPod)= 10/30
P(PC)= 16/30
P(Both iPod and PC)= the only value in both categories / the overall total= 4/30
P(iPod OR PC)= P(iPod) + P(PC) - P(Both) = (10/30)  +  (16/30)  - (4/30) = 22/30
OR I could just count all values in the ipod or the PC categories without counting any numbers twice and divide that by the total to get the probability of owning an iPod or a PC... (2+4+10+6)/30 = 22/30


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