Skip to main content

Challenge 113: Dice Scores

Can you find the probability that the highest score shown is more than twice as much as the lowest score?

I have three ordinary unbiased cubical dice; one is green and the others are red.

I throw all three dice, and note the score on the green die along with the lowest score shown on either of the red dice.

What is the probability that the score on the green die is more than twice the lowest score on either of the red dice?

I decide to ignore the colours of the dice, and just note the highest and lowest scores shown on any of them when they are thrown.

What is the probability that the highest score shown is more than twice as much as the lowest score shown?