Remember Me?

 Straight Dope Message Board Remember Me?

#1
10-06-2016, 09:41 AM
 Skammer Charter Member Join Date: Aug 2002 Location: Music City USA Posts: 14,055
Odds problem - roll a pair of dice

A math teacher friend of mine shared this problem on Facebook and we are disagreeing about the solution. Here is the problem verbatim:

"Two fair dice are rolled together, and you are told that 'at least one of the dice is a 6.' A 6 is removed, and you are ten shown the other die. What is the probability of the other die showing a six?"

My friend thinks the answer is 1/6, because the dice rolls are independent events and regardless of what one shows, the other has a 1/6 chance of being a six. I'm quite positive this is incorrect.

My reasoning is: if you roll a pair of dice, there are 36 possible combinations: (1,1), (1,2), (2,1), etc. Out of these 36 combinations, 11 contain at least one six: each 6 paired with 1-5 on the other die, and double sixes.

Since we are told that the pair contains at least one six, we have 11 possible combinations with equal chance of occurring. If a six is then removed, only 1 of the remaining 11 dice is another six. So I maintain the answer is 1/11.

However, the meme that she posted is multiple choice and 1/11 is not one of the available answers, which are: 1/18, 1/36, 2/11 and 1/6.

At first I jumped on the 2/11 thinking "there are two chances to pick a six from the pair of doubles!" But that logic falls apart I think. I'm back to 1/11. How am I wrong?

 Bookmarks

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is Off HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Main     About This Message Board     Comments on Cecil's Columns/Staff Reports     General Questions     Great Debates     Elections     Cafe Society     The Game Room     Thread Games     In My Humble Opinion (IMHO)     Mundane Pointless Stuff I Must Share (MPSIMS)     Marketplace     The BBQ Pit

All times are GMT -5. The time now is 04:00 AM.

 -- Straight Dope v3.7.3 -- Sultantheme's Responsive vB3-blue Contact Us - Straight Dope Homepage - Archive - Top

Send questions for Cecil Adams to: cecil@straightdope.com