0
$\begingroup$

$C$ and $J$ play a game. $C$ always starts. $C$ rolls a fair dice first and wins if he throws an even number. If not, then $J$ rolls the dice. If she rolls an odd number she wins. if neither win it's a draw. a) What is the probability of the game being drawn? b) Is this game fair? If they played the game $100$ times how many games should $J$ win?

$\endgroup$
  • $\begingroup$ What have you tried? Note that these rolls are just like flipping a coin, as even and odd each have probablity $1/2$ There are only three possible outcomes, so write them all down and assess the probabilities. $\endgroup$ – Ross Millikan May 20 '15 at 21:48
1
$\begingroup$

Hint: If the game was fair then the probability that $J$ wins should be $1/2$, since that is the probability that $C$ wins. But a draw is possible. This can also help you figure out the last part of the problem.

$\endgroup$
0
$\begingroup$

a) The probability of a draw is simply that C rolls an odd number and J rolls an even number, i.e. it is $0.5\cdot0.5=0.25$.

$\endgroup$
  • $\begingroup$ First of all, thank you for existing. Next thank you for answering my question but what's the logic? My assumption was that a win & a lose would be 3/6. Why am I wrong? $\endgroup$ – user242253 May 20 '15 at 22:02
  • $\begingroup$ Well, you have two players here and each of them rolls the dice independently. C has a probability of winning of 50 percent (3/6). The same applies to J, but he only plays after C, so only when C loses first. $\endgroup$ – dsforecast May 20 '15 at 22:05

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.