### Brain Teasers

# Game of Dice

Probability
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

Let's play a game: we'll roll two dice. If a 3 appears on either die, then we will pick them both up and re-roll them. If not, then we'll add them together. If the sum of the two dice is even, I win, and if the sum is odd, you win. What is the probability you'll win? What is the probability I'll win?

### Answer

The probability I'll win is 13/25The probability you'll win is 12/25

There are 36 possibilities when rolling two dice, 18 odd and 18 even. 11 of those possibilities have a 3 involved on at least one die and are excluded in this game. Five of the excluded possibilities are even and six are odd. This leaves us with 13/25 probability of an even number and 12/25 probability of an odd number.

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## Comments

Good teaser. It seems really odd that even would win!

What Jimbo, even though you know odd would win, even then it seems odd?

Well, you had an even chance of answering the odd teaser correctly, at least half of it.

Good teaser!

Good teaser!

I only found 21 possibilities. Where are the others?

nice teaser!

I bet Ms50cent can do batter than dat.

but one of the evens is 3 and 3, so wouldnt that get re rolled?

That was fun, but not too hard!

Possible rolles....

1st Dice is 1, 2nd dice is 1,2,4,5,6

Totals = 2, 3, 5, 6, 7

1st dice is 2, 2nd dice is 1,2,4,5,6

Totals = 3, 4, 6, 7, 8

1st dice is 4, 2nd dice is 1,2,4,5,6

Totals = 5, 6, 8, 9, 10

1st dice is 5, 2nd dice is 1,2,4,5,6

Totals = 6, 7, 9, 10, 11

1st dice is 6, 2nd dice is 1,2,4,5,6

Totals = 7, 8, 10, 11, 12

Add up the number of even totals:

2,6, 4,6,8,6,8,10,6,10,8,10,12 = 13

Add up the number of odd totals:

3,5,7,3,7,5,9,7,9,11,7,11 = 12

As you can see, there's 13/25 even numbers and 12/25 odd numbers.

As you can see, the answer is correct.

1st Dice is 1, 2nd dice is 1,2,4,5,6

Totals = 2, 3, 5, 6, 7

1st dice is 2, 2nd dice is 1,2,4,5,6

Totals = 3, 4, 6, 7, 8

1st dice is 4, 2nd dice is 1,2,4,5,6

Totals = 5, 6, 8, 9, 10

1st dice is 5, 2nd dice is 1,2,4,5,6

Totals = 6, 7, 9, 10, 11

1st dice is 6, 2nd dice is 1,2,4,5,6

Totals = 7, 8, 10, 11, 12

Add up the number of even totals:

2,6, 4,6,8,6,8,10,6,10,8,10,12 = 13

Add up the number of odd totals:

3,5,7,3,7,5,9,7,9,11,7,11 = 12

As you can see, there's 13/25 even numbers and 12/25 odd numbers.

As you can see, the answer is correct.

Very good teaser. And correct, I might add.

wew.. i didnt notice that there are two die. i thought that it is only one die which is rolled so my answer is,

the probability i win is 1/3

the probability you win is 1/2

haha..nice teaser

the probability i win is 1/3

the probability you win is 1/2

haha..nice teaser

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