Question

You have two six-sided fair dice. One of them is a regular fair dice one numbered from 1 to 6. The other one is blank on all sides. How do you number all faces of the blank one (with whole numbers, repetition is allowed) such that when you roll both dice, the sum of the numbers that show up on both dices ranges between 1 and 12 (both inclusive) with equal probability?

Answer 1

Answer:

Numbers - {0,1,2,4,5,6}

Step-by-step explanation:

Max. no. on given dice = 6

∵ Max. possible sum = 12

Max possible no. on blank dice, M = 12 - 6 = 6

Similarly,

Min. no. on given dice = 1

∵ Min. sum possible = 1

Min. possible no. on blank dice, N = 1 - 1 = 0

Now,

The no. to be removed to get equal probability

= ( M + N ) / 2

= 6 / 2

= 3

∴ Range of Set of Numbers = 0 - 6

∴ Set of Number = {0,1,2,4,5,6}