Question 1189464
.
A box contains red, blue and green pens. If one pen is chosen at random, the probability that a red pen will be chosen is two times the probability for
a blue pen and three times the probability for a green pen. If there are 12 red pens in the box, how many pens are in the box?
~~~~~~~~~~~~~


<pre>
Let x be the number of pens, in total.


Then the probability to get red pen is {{{12/x}}};

and two other probabilities are  {{{6/x}}}  and {{{4/x}}}, according to the problem.


The sum of probabilities is 1, so


    {{{12/x}}} + {{{6/x}}} + {{{4/x}}} = 1.


It gives  12 + 6 + 4 = x,  hence,  x = 22 :  there are 22 pens, in all.
</pre>

Solved.