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I'm here again, and now with more doubts on algebra on probability functions;

$Let$ $\Omega{{a1, a2, a3}}, $find $ P(a1) $whether: $P(a1) = 2*P(a2) $ and $ P(a3) = \dfrac{1}{4}$

I've got now after notice that $P(a1) + P(a2) + P(a3) = 1$ that $P(a1) + 2*P(a2) = \dfrac{3}{4}$ but I've got stuck on this;

what I do now ? Thanks in advance.

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What you do now is learn how to accept answers, and then do it! – Gerry Myerson Apr 12 '12 at 0:26
up vote 1 down vote accepted

You did not substitute the information $P(a_1)=2P(a_2)$ correctly.

You should start by writing $$ \color{maroon}{P(a_1)}+P(a_2)+\color{darkgreen}{P(a_3)}=1\iff \color{maroon}{2P(a_2)} +P(a_2)+\color{darkgreen}{{1\over 4}}=1. $$ Of course, finish by solving the equation on the right hand side of the above for $P(a_2)$. Then you can find $P(a_1)$.

Alternatively you could start with $$ {P(a_1)}+\color{maroon}{P(a_2)}+\color{darkgreen}{P(a_3)}=1\iff {P(a_1)} +\color{maroon}{{1\over 2}\cdot P(a_1)}+\color{darkgreen}{{1\over 4}}=1. $$

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Thanks a lot, I didn't looked at this way! – aajjbb Apr 12 '12 at 0:05

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