Given that i have 6 pairs of balls where each pair contains 2 balls of the same colour in the bag. So the bag would contain RR, GG, BB, PP, YY, WW (red, green, blue, pink, yellow, white).
Whats the probability of finding atleast one pair when
a) 1 Ball has been drawn out
b) 2 Balls have been drawn out
c) 3 Balls have been drawn out
d) 4 Balls have been drawn out
etc up to 12 balls in total,
I'm not necessarily looking for the answer but rather the methodology behind solving a problem like this.
Thanks!
Best Answer
The idea: you can come up with the probability in each case by way of $$ P(\text{at least one pair in $k$ drawn})=\frac{\text{# of ways of choosing $k$ balls w/ a pair of same color}}{\text{# of ways of choosing $k$ balls}}. $$
As a hint: note that this is the same as $$ P(\text{at least one pair in $k$ drawn})=1-\frac{\text{# of ways of choosing $k$ balls of different colors}}{\text{# of ways of choosing $k$ balls}}, $$ which might be much easier to compute.