The Motley Fool Discussion Boards Previous Page Fun & Games / Math Recreations & Puzzles URL:  https://boards.fool.com/bob-there-are-3-dice-in-a-bag-6-sided-12-sided-34612741.aspx Subject:  Re: Probability problem Date:  9/8/2020  12:51 PM Author:  rev2217 Number:  5999 of 6013 Bob, There are 3 dice in a bag: 6-sided, 12-sided and 20-sided. We pick one die at random, roll it, and it gives us a number N. What's the probability that when we pick another die and roll it, we'll get a number smaller than N, if N = 4? This problem actually is much simpler than it appears. Regardless of which die is pulled first and whether it's replaced or not, there's a 1/3 probability of picking each die on the second selection. Each die has 3 faces that are less than 4 (values 1, 2, and 3). Thus, the probability is P = 1/3 x 3/6 + 1/3 x 3/12 + 1/3 x 3/20 = 1/6 + 1/12 + 1/20 = (10+5+3)/60 = 18/60 = 3/10.Norm. Copyright 1996-2021 trademark and the "Fool" logo is a trademark of The Motley Fool, Inc. Contact Us