**Let"simagine you are playing a game which uses dice. You are about to rollthree of them. You NEED to roll at least one 6. A 6 appearing onany one (or more) of the three dice will win the game for you! What areyour chances?** **33.3%** **42.1%** **50%** **66.6%** **Quitesome time ago, I was over at a friend"s house watching him and anotherfriend play a board game called ****Axis & Allies.****At one point this exact scenario came up - Kent was planning on rollingthree dice and ****really****wanted at least one 6 to appear. He made a comment that with threedice, his chances were 3****/****6 or 50%.** **Kent"sreasoning was, with one die, the chances of rolling a 6 were 1****/****6 which is correct. Healso believed if he were to roll two dice, his chances were double thisor 2****/****6. This is INCORRECT andthis is where his faulty reasoning begins.** **Knowinga little bit about the laws of probability, I quickly knew the fraction"2****/****6" for two dice and "3/6" for three dice was incorrect and spent a brief moment computing and then explaining the true percentages. Unfortunately, I do notbelieve I was successful in explaining to Kent why my figures werecorrect. Maybe I can do so here. The knowledge gained could certainly be very useful if you wish toplay free craps games.** **Obviously,with Kent"s logic above, if the chances of rolling a 6 with two dice is2****/****6 and the chances ofrolling a 6 with three dice is 3/6, then the chances of rolling a 6with six dice would be 6****/****6 !! 100%?? Of course, this is obviouslyincorrect. I don"t care how many dice you roll, the chances of rollinga 6 will never be 100%.** **Whenyou roll just one die, there are six different ways the die can land,as shown by the following graphic:** |