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The Probability of Outcomes

Date: 20 Feb 1995 10:03:29 -0500
From: Anonymous
Subject: Probability


Could you help with this problem?

In the sample space for a probability experiment, outcome A is twice 
as likely as outcome B. Outcome C is two-thirds as likely as outcome B. 
Outcome C is twice as outcome D.  Find the probability of each outcome 
in the sample space.

Sample Space   {A,   B,   C,  D}
Probability     |    |    |   | 

Any consideration given this request will be appreciated. 

Date: 20 Feb 1995 10:40:34 -0500
From: Dr. Ken
Subject: Re: Probability

Hello there!

If the four outcomes, A, B, C, and D are the only possible outcomes for 
the experiment, then we can do this problem.  Let's call the probability 
of outcome D by the letter, d.  Then we have c=2d, c=2b/3 so b=3d, and 
a=2b so a=6d.  Because the sum of the probabilities of all the different 
outcomes must be 1, we have a+b+c+d=6d+3d+2d+d=12d=1, d=1/12.  Thus,
we can plug this value back into the expressions we got for a in terms of 
d, b in terms of d, and c in terms of d, to find out what the individual 
probabilities are. 

I hope this helps!

-Ken "Dr." Math
Associated Topics:
High School Probability

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