Suppose you have a bag with 10 black and 10 red balls, with the balls of each color numbered 1 to 10. Suppose you pick two balls uniformly at random from the bag. a. Show that the probability that you pick a ball of each color is 10/19.
b. Show that the probability that you pick a ball of each color, with the number on the red ball being one less than the number on the black ball, is 9/190.