Question

http://gyazo.com/67e899ab3acedaeecf3e17adbc8a6cfc

Answer 1

Let there be n red marbles in the bag.
P(getting 16 red marbles) = 48C16 (n/45)^16 ((45-n)/45)^29
This probability needs to be very high.
We need to maximize it
http://www.wolframalpha.com/input/?i=maximize+C%2848%2C16%29+%28n%2F45%29%5E16+%28%2845-n%29%2F45%29%5E29++

Answer 2

You infact only need to find that value of n for which n^16 * (45-n)^29 is max
f(n) = n^16 * (45-n)^29
f'(n) = n^15 * (45-n)^28 (16 (45-n) - 29n)
SInce n >0 and n<45 is our basic assumption, we get f'(n) = 0 only when
16(45-n) = 29n
or n=16
f"(16) <0, hence this must be a point of maxima