## February 18, 2009

### Dice problem

Two people are playing with a pair of dies. Instead of numbers,
the dies have different colors on their sides. The first person wins
if the same color appears on both the dies and the second person
wins if the colors are different. The odds (chance)of their winning
are equal. If the first dice has 5 red sides and 1 blue side,
find the color(s) on the second one.

[really tough one]

Secret SquÃ¯rrel said...

Interestingly, the second die should have 3 red sides and 3 blue. From this you can surmise that it doesn't actually matter what the first die looks like.

Without writing out all of the possible combinations, it can be seen that if the first die comes up "blue", the second die will match it half of the time (B-B) and not match half of the time (B-R). This will give each player the same odds of winning.

Likewise, if the first die comes up "red", the second die will still match it half of the time (R-R) and half not (R-B).

Michel said...

totally agree 3:3

Ashish said...

The second dice (assuming only red and blue colors)
assume x red and (6-x) blue
equating the probablity we get
(5/6).(x/6)+(1/6).((6-x)/6)=(5/6).((6-x)/6)+(1/6).(x/6)

x=3 & (6-x)=3

alina said...

yes totally

Anonymous said...

its not hard when there are only 4 possible answers lol