(adsbygoogle = window.adsbygoogle || []).push({}); Dice with weighted sides, looking for odds of a sum:faster way plz

1. The problem statement, all variables and given/known data

6 side die is weighted so prob of rolling 2,3,4,5,6 is same and rolling 1 is 3x rolling a 2. If die is thrown twice, what's odds of getting a sum of 4?

2. Relevant equations

3. The attempt at a solution

x+x+x+x+x+3x represents the "chances" of rolling a 2,3,4,5,6, and 1. So 2,3,4,5,6 individually have a 1/8 chance of rolling each time. 1 has a 3/8 chance of hitting each time.

a)For sum of 4 from 2 rolls, I need to get 1,2,3 on either rolls. Chance of getting that on first roll is 1/8 + 1/8 + 3/8 = 5/8.

If I get a 1 or 2 on first roll, then my 2nd roll can only be one result, so 5/8*1/8=5/64. Then now it's weird. If I get a 3, I multiply 5/8 by 3/8 right?Answer is 7/64though and for 3, it'd be 15/64.

Also, 7/64 doesn't match the 5/64 I got for getting a 1 or 2 on 2nd roll.

b)I made a chart. I got the correct answer this way, but can someone show me a faster way?

http://s000.tinyupload.com/index.php?file_id=15919977748640328011

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# Homework Help: Dice with weighted sides, looking for odds of a sum:faster way

**Physics Forums | Science Articles, Homework Help, Discussion**