Find the odds of rolling a pair of dice and getting a sum
of 11 or greater
Here are all possible rolls:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
The rolls with sum 11 or greater are in red,
and the ones not with sum 11 or greater are
in blue. The odds in favor of red are
"reds:blues". We count the red ones. There are
3. We count the blue ones. There are 33.
So the odds in favor are 3 to 33 or 3:33
and we can divide both by 3 and get 1:11,
which is read as "1 to 11".
[Note: If you had been asked for the odds against
instead of the odds in favor, the odds against are
33 to 3 or 33:3 and we can divide both by 3 and
get 11:1, which is read as "11 to 1".
If you had been asked for the probability instead
of the odds in favor, the probability would be 3 out of 36,
or 3/36 which reduces to 1/12.]
Edwin
