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The probability that a six sided (possibly loaded) die lands on the ith face is [itex] P_i [/itex]. The [itex] P_i [/itex] are unknown. We are given the values of [itex] S_i [/itex] = the probability that the [itex]i[/itex]_th face is first to land 100 times in a sequence of independent tosses of the die. Find the [itex] P_i [/itex] as functions of the [itex] S_i [/itex].