# algebra

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two dice are rolled. if a 3 appears on either dice,then the two dice are rolled again and the two dice are added togather. if a 3 does not appear, then we ll add the two dice togather. if the sum of two dice is even ,i win and if the sum is odd,you win. what is the probability that you win? what is the probability that i winn/

• algebra -

It doesn't matter whether the 3 appears or not on the dice in the first roll. What matters is whether the sum of the winning roll is even or odd.

The sum will be odd if one dice is an even number, and one dice is an odd number

The sum will be even if both dice are even or both dice are odd.

The probability of any dice being even is 1/2

The probability of any dice being odd is 1/2

The probability of the first dice being even and the second dice being even is 1/2 * 1/2 = 1/4

The probability of the first dice being odd is 1/2 * 1/2 = 1/4

The probability of the first dice being even and the second being odd is 1/2*1/2 = 1/4

The probability of the first dice being odd and the second being even is 1/2*1/2 = 1/4

Therefore the probability of an even sum (even, even) or (odd,odd) is 1/4+ 1/4 = 1/2

And the probability of an odd sum (even, odd) or (odd, even) is 1/4+1/4 = 1/2

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