Q5. You have 17 red and 17 blue balls, and you remove 2 at a
time. If the two are the same colour, add in on extra blue abll. If
they are different colours, add in an extra red ball. What colour
is the final ball removed?
Ans : Red ball. Reasoning: Following the path of highest
probability, first draw would be (r,b). So -(r,b), +1 r. box left
with 17r, 16 b, 33 balls in total. 2nd draw : (r,r) and
(r,b) have equal chances of occuring. (b,b) lowest chance. By
charting the paths of the highest probability draws and their
outcomes, we will notice that, by the 4th draw, all outcomes will
be the same: 15r, 15b, 30 balls in total, and only one
subsequent highest probability draw : (r,b). This mirrors the
starting scenario when : ratio r:b = 1,1 and subsequent draw
=(r,b). hence 4 draws = 1 cycle. 34 draws, so 8 complete cycles
which means 32 draws. After the 32th draw, box left with 2
balls; 1r , 1b, as predicted in the pattern of the
cycle. next draw (r,b). add one red ball. No choice, next draw
that sole red ball is removed.
Pardon me if im wrong, i could have made a careless mistake
in my working. If this is an interview question, it would be
rather impossible to answer on the spot. i had to use pen and paper
to work this out, and it took me quite awhile.
