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I'm dealing with a problem in probability, there's:

Let P be an probability function in $\Omega{\{a1, a2, a3\}}$, find $P(a1)$ whether:

$P(a2) = \dfrac{1}{3}$ and $P(a3) = \dfrac{1}{4}$

I don't even know from where to start, since I'm a beginner in probability;

Thanks in advance;

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Do you mean ‘find $P(a1)$ if $P(a2)=\frac13$ and $P(a3)=\frac14$’? If so, use the fact that $P(a1)+P(a2)+P(a3)=1$: the probabilities of the individual outcomes must add up to $1$. – Brian M. Scott Apr 11 '12 at 1:24
Three things: this would look a lot better if you tex it, you should go back and accept answers to your previous questions (you'll get more help if you do), and as a hint, what is $P(\Omega)$? Using that $\Omega - (\{a_2\}\cup\{a_3\}) = \{a_1\}$ what does that tell you? – Chris Janjigian Apr 11 '12 at 1:25
up vote 2 down vote accepted


  1. $P(\{a_1,a_2,a_3\})=1$
  2. $P(A \cup B)=P(A)+P(B)$ whenever $A \cap B =\varnothing$.
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Thanks everybody, I now I've noticed that the sum of events is equal 1, thanks; – aajjbb Apr 11 '12 at 2:51
@aajjbb then please accept the solution (and solutions to your previous problems) – Chris Janjigian Apr 11 '12 at 3:08
Do you know about accepting answers to your questions? Do you understand why it's considered a good idea to do so? Please go through the faq if you are unsure. – Gerry Myerson Apr 11 '12 at 4:21

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