SOLUTION: Two fair dice are rolled. Find the odds for rolling a sum of 10.
Now find the odds against rolling a sum of 10.
(I am unsure how to mathematically do this, a step by step e
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Question 1071563: Two fair dice are rolled. Find the odds for rolling a sum of 10.
Now find the odds against rolling a sum of 10.
(I am unsure how to mathematically do this, a step by step explanation would be greatly appreciated to help me on the rest of my homework!)
Found 2 solutions by Boreal, josmiceli:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
There are 36 outcomes, 6 from each die, and they are independent.
Of those 36, 3 are 10 (5-5,6-4,4-6)
The probability of a 10 is the number of times it is rolled/number of possibilities
That is 3/36 or 1/12.
---------------------------
The odds is the ratio of the number of successes over the number of failures, and that is 3/33 or 1/11. Probability is constrained between 0 and 1; odds between 0 and infinity.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The ways of getting 10 with 2 dice are
6 and 4
4 and 6
5 and 5
-----------
so there are 3 ways of getting 10
Each of the 6 faces of one die can be paired up with
one of the 6 faces of the other die, so there are
possible outcomes
------------------------------
The odds are defined as:
[ outcomes you want ] : [ outcomes you don't want ]
The odds of getting a 10 are:
3:33
The odds of not rolling 10 are:
33:3
----------------
This is an easy example. Let's say you had dice each with
100 faces, 1 through 100, and you wanted odds that
when rolling them, you would get a total of 150. You would
have:
100 & 50
50 & 100
-----------
99 & 51
51 & 99
-----------
etc. until you get to:
75 & 75
which is the last one
So, there must be a mathematical rule.
It looks like:
Total of outcomes you want is:
(( # of faces ) minus ( total you want/2 ))*2 + 1
Maybe you can look up a "formal" method.
Or you can figure it out each time like this.
Definitely get another opinion, too.
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