A bowl contains 10 red balls and 10 blue balls, A women selects ball at random without looking? How can we solve this question ?
A bowl contains $10$ red balls and $10$ blue balls, and a women picks up 
balls from the bowl, at random, without looking. 
A) How many balls must she pickup in order for her to be sure she is holding at least $3$ balls of the same color?
B) How many balls must she pickup in order for her to be sure she is holding at least $3$ blue balls ?
 A: Worst case scenario for A) is picking up alternating colors, and thus she can only be sure she holds $3$ balls of the same color after $5$ pickups.
After pickup $1$ and $2$, she obviously doesn't have $3$ of the same color.
After pickup $3$ she may have $(2,1)$ (each number in the bracket stands for the number of balls of a given color).
After pickup $4$ she may have $(2,2)$.
After pickup $5$ she may have $(5,0)$ or $(4,1)$ or $(3,2)$, hence at least $3$ of one of the colors.  
Regarding B), worst case scenario is that the first $10$ balls are red.. So in order to be sure she has $3$ blue balls, she needs to pickup $13$ times.
A: Here are a couple of hints:
A) Let's say she draws 4 balls.  Can she be sure of having three of the same color?  Why or why not?
B) Let's say she draws 10 balls.  It's likely that there will be three blue in the mix, but we're looking for a guarantee.  Will 10 balls guarantee three blue?
A: $(A)$  If she selects $>2+2$  balls, $3$ of them must be of same color
$(B)$ If she selects  $>10+2$ balls, in the worst case, after $10$ red balls, rest must be blue
