# Thread: Dice probability with limited reroll

1. ## Dice probability with limited reroll

Hello,

I'm having difficulty understanding this problem and I was wondering if someone had an answer.

Let

The probability of getting 2 success if each die is rolled only once is

If we have the option to reroll any failed die once,
then
and

What is the probability if we can reroll only one failed die (instead of all 3)?

2. ## Re: Dice probability with limited reroll

Out of the 3 dice, 2 are rolled once and 1 die is rolled twice

The probability of rolling 2 successes when all three dice are rolled and then one is rerolled is:

+

+

+

However, this seems wrong because it's greater than if I were to roll 3 dice with rerolling

What am I missing?

P.S. Sorry for the formatting. The tex on this site doesn't support \binom{x}{y} nor the '+' sign.

3. ## Re: Dice probability with limited reroll

Originally Posted by Dan K
P.S. Sorry for the formatting. The tex on this site doesn't support \binom{x}{y} nor the '+' sign.

Use math tags instead of tex tags and things will work better.

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