Question 1105352
<pre>
We want the probability that the ball came from box M, 
given that it is even:

{{{matrix(1,3,
"P(M|EVEN)",
""="",
matrix(1,3,"P(M","and","EVEN)")/"P(EVEN)")}}}

The probability of choosing box M is 1/2.
The probability of then getting an even ball (from box M) is 4/9,
So 

{{{matrix(1,5,
matrix(1,3,"P(M","and","EVEN)"),
""="",
(1/2)(4/9),
""="",
2/9)}}}

{{{matrix(1,13,

P(EVEN),
"",
""="",
"",
matrix(1,3,"P(M","and","EVEN)"),
""+"",
matrix(1,3,"P(N","and","EVEN)"),
"",
""="",
"",
4/9,
""+"",
matrix(1,3,"P(N","and","EVEN)") )}}}

The probability of choosing box N is 1/2.
The probability of then getting an even ball (from box N) is 2/5,
Therefore,

{{{matrix(1,5,
matrix(1,3,"P(N","and","EVEN)"),
""="",
(1/2)(2/5),
""="",
1/5)}}}

Therefore,

{{{matrix(1,15,

P(EVEN),
"",
""="",
"",
4/9,
""+"",
matrix(1,3,"P(N","and","EVEN)"),
"",
""="",
"",
4/9+1/5,
"",
""="",
"",
29/45)}}}

Therefore,

{{{matrix(1,17,
"P(M|EVEN)",
"",
""="",
"",
matrix(1,3,"P(M","and","EVEN)")/"P(EVEN)",
"",
""="",
"",
(2/9)/(29/45),
"",
""="",
"",
(2/9)(45/29),
"",
""="",
"",
10/29)}}}

Edwin</pre>