25 balls (Posted on 2008-09-25)

	Submitted by pcbouhid
No Rating
Solution:	(Hide)
Since it was said "three bals at random (without looking), itīs intuitive that we are dealing with no replacement. The probability of winning is 1529/2300 or 66,478%. We first need to count the number of possible outcomes there are to our game of drawing 3 balls from the bin. Recall that the number of ways to choose k objects from a set of n objects is C(n,k) = n! / [k!(n-k)!]. In our case, we are choosing 3 balls from a set of 25 balls, so the number of choices is C(25,3) = 25! / [3!22!] = [25*24*23] / [3*2] = 2300. Now we just need to figure out how many of those possible choices will win the game. In order to win we need to do one of three things: (1) draw exactly 2 red balls (with the third ball being some other color); (2) draw exactly 2 yellow balls; or (3) draw exactly 2 blue balls. To choose exactly two red balls amounts to choosing two balls from the set of 10 red balls, followed by picking any of the 15 non-red balls as the third choice. So, the number of ways to choose exactly 2 red balls is C(10,2)*15 = 45*15 = 675. Similarly, the number of ways to choose exactly 2 yellow balls is C(8,2)*17 = 28*17 = 476. And the number of ways to choose exactly 2 blue balls is C(7,2)*18 = 21*18 = 378. So, the total number of winning choices is 675 + 476 + 378 = 1529. So, the probability of winning this game is 1529/2300 = 66,478%.

	Subject	Author	Date
	Puzzle Thoughts	K Sengupta	2023-03-20 09:57:59
	re(2): Solution: With and Without Replacement	Russ	2008-09-26 13:14:43
	re: Solution: With and Without Replacement	Syzygy	2008-09-26 10:27:32
	Solution: With and Without Replacement	Russ	2008-09-26 02:41:47
	Ah, yes...	ed bottemiller	2008-09-25 13:04:15
	Solution?	ed bottemiller	2008-09-25 12:24:45
	solution	Charlie	2008-09-25 12:21:40
	Solution	Dej Mar	2008-09-25 12:16:35