Question 1012310
Mike determined that some children like to eat cake, some like 
to eat cookies, and others don't like to eat cake or cookies. 
He calculated the probabilities and created the Venn diagram 
below:

a venn diagram showing two categories, cake and cookies. In the 
cake only circle is 0.2 in the cookies only circle is 0.5, in 
the intersection is 0.1, outside the circles is 0.2

What is the probability that a child eats cake, given that he/she 
eats cookies?
<pre>
{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,0.2),locate(1.5,1.7,0.5),locate(-3.7,-1,0.2), locate(-3.2,4,CAKE), locate(-.25,1.8,0.1),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(2.5,4,COOKIES)
 )}}}

The conditional probability formula for the probability
of A given B is 

{{{matrix(1,3,

P(matrix(1,3,A,"|",B)),

""="", 

P(matrix(1,3,A,and,B))/(P(B))
            

)     }}}

So we have:

{{{matrix(1,9,

P(matrix(1,3,CAKE,"|",COOKIES)),

""="", 

P(matrix(1,3,CAKE,and,COOKIES))/(P(COOKIES)),

""="",

0.1/(0.1+0.5),

""="",

0.1/0.6,

""="",

1/6
            

)     }}}

Edwin</pre>