Broken Dice Game - 223355 vs. 114466

Probability Level 2

Doug and Mattie are playing a game using strange dice. Each die is a cube with six sides. Doug's die has sides numbered 2, 2, 3, 3, 5, and 5. Mattie's die has sides numbered 1, 1, 4, 4, 6, and 6.

To play the game, Doug and Mattie roll their dice at the same time and whoever rolls the higher value wins. If they play many times, who will win more frequently, Doug or Mattie?

Both are equally likely to win Mattie Doug

4 solutions

Hadia Qadir
Aug 12, 2015

P(Doug) = 16/36; P(Mattie) = 20/36, so MATTIE wins.

Trevor B.
Aug 9, 2015

When Doug rolls a $2,$ he has a $\frac{1}{3}$ chance of winning (Mattie throws a $1$ ). When Doug rolls a $3,$ he has a $\frac{1}{3}$ chance of winning (Mattie throws a $1$ ). When Doug rolls a $5,$ he has a $\frac{2}{3}$ chance of winning (Mattie throws a $1$ or a $4$ ).

All of the above cases, are equally likely, so the probability Doug wins is equal to the average of his chances of winning in each case. $\frac{\frac{1}{3}+\frac{1}{3}+\frac{2}{3}}{3}=\frac{\frac{4}{3}}{3}=\frac{4}{9}$ Doug's probability of winning is less than $\frac{1}{2},$ so he is more likely to lose, meaning $\boxed{\text{Mattie}}$ is more likely to win.

Moderator note:

Simple direct approach of counting total positive cases.

Moutazz Alaref
Aug 7, 2015

we have 6 6=36 p. for "Doug" to win (2 make him win twice ,so 2 2=4),

and(3 make him win twice 2*2=4)

and(5 make him win 4 times 4*2=8) , So his chance =16/36 .

(if you calc. for "Mattie" , you get his chance=20/36.

SO "Mattie" wins ..

Rakibul Hyder
Aug 14, 2015

It can be thought in an easy way..Doug has 4 ways to win while Mattie has 5 ways.

Not correct. 5 ways may have lesser probabilty of occurring than 4 ways.

Aditya Raman - 5 years, 10 months ago

Broken Dice Game - 223355 vs. 114466

4 solutions

Moderator note:

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