Suppose now that I have two dice, with 12 and 20 sides respectively. I will keep

Question

Suppose now that I have two dice, with 12 and 20 sides respectively. I will keep rolling both dice together until l see the same number on both dice. What is the expectation of the number of times I will roll the dice? 12 10 20 1/2 6 1 Suppose I roll n fair dice, each of which has 20 sides. What is the expected number of pairs of dice that show the same number? Now write the number of colliding pairs as a sum of indicator variables, one for each pair, where the indicator for a given pair is 1 if that pair collides. n/20 n(n - 1)/40 (n 2) 100 n/800 n(n - 1)/800

Explanation / Answer

a)Probabilty of same number in both dice = 12*(1/12)(1/20) = 1/20

Expected no of rolls =1/(1/20) = 20

b)probabity that given pair has same number = 20*(1/20)(1/20) = 1/20

total no pairs = n(n-1)/2

Expected no of pairs = (1/20)*(n(n-1)/20) = n(n-1)/80

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