Suppose you roll a fair six sided die repeatedly until the

Question

Suppose you roll a fair six sided die repeatedly until the first time you roll a number that you have rolled before.

a) For each r = 1, 2, . . . calculate the probability pr that you roll exactly r times,

b) Without calculation, write down the value of p1 + p2 + . . . + p10. Explain.

c) Check that you calculated values of p_r have this value for their sum.