Question

Consider the experiment of rolling six 6-sided dice. The sample space S is all length-6 sequences made up of integers 1 to 6, with replacement. (a) Find the probability of all dice yielding the same number. (b) Find the probability that all the numbers are distinct.

Answer 1

a) Probability of all dice yielding the same number is computed here as:

= Number of ways to select a number which would be same in all the 6 dice * Probability to get that same number in all 6 dice

= 6*(1/6)⁶ = (1/6)⁵

Therefore (1/6)⁵ = 0.000129 is the required probability here.

b) Probability that all numbers are distinct is computed here as:

Number of ways to get all numbers distinct / Total number of combinations in rolling 6 dices

= Permutation of 6 distinct numbers / Total number of combinations in rolling 6 dices

= (6*5*4*3*2*1) / 6⁶

= 0.0154

Therefore 0.0154 is the required probability here.