Question 394011
We assume that {{{k>= 2}}}, or else the event of getting 2 white marbles is excluded.

The probability of getting 2 red marbles  = {{{3C2/(k+3)C2}}}
The probability of getting 2 white marbles  = {{{kC2/(k+3)C2}}}
Hence 
{{{3C2/(k+3)C2 + kC2/(k+3)C2 = 1/2}}}
<==> {{{6/((k+3)(k+2)) + (k(k-1))/((k+3)(k+2)) = 1/2}}} after simplifying.
<==> {{{(k^2 - k + 6)/(k^2 + 5k + 6) = 1/2}}}
<==> {{{k^2 - 7k + 6 = 0}}}, after cross-multiplying and simplifying.
<==> (k-1)(k - 6) = 0.
==> k = 1, 6.
Therefore k = 6, the number of white marbles.