0
$\begingroup$

A and B play a game with two six-sided dice. Each die has some red faces and some blue faces. The two dice are thrown simultaneously. If the top face of each die is the same color, A wins, and if they are different colors, B wins. One die has five red faces and one blue face. How many red faces does the other die have if both players have the same chance of winning?

$\endgroup$
  • $\begingroup$ Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. $\endgroup$ – José Carlos Santos May 2 at 7:07
2
$\begingroup$

If there are $r$ red and $b$ blue faces on the second die, then A will win with probability $$\frac56\cdot\frac r6+\frac 16\cdot\frac b6. $$ This is supposed to be $\frac12$, and of course $r+b=6$. Solve these equations.


Once you solved the problem that way, perform an excessive (contactless) facepalm and contemplate why you didn't see the solution right away without computation.

| cite | improve this answer | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.