Two balls are chosen at random from a box containing 12 balls, numbered 1, 2, ..., 12. Let X be the larger of the two numbers obtained. Compute the PMF of X, if the drawing is done a.) with replacement b.) without replacement
I'm having trouble with finding an easier way to solve the second part of this problem. I understand that the total number of outcomes is 12*12, this is the denominator, but the numertaor, favorable outcomes, is giving me trouble. I know the answer is 2x-1 but I figured this out by seeing a pattern for each possible outcome. Is there an easier way to deduce this answer? How can I get that there is 2x-1 without haveing to write out every single outcome and looking for a pattern? Please don't just say there are 2x-1 choices. I want to understand the thought process. In otherwords how did you arrive at this.