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4

Part of 1997 Argentina National Olympiad

Problems(1)

first 1997 natural numbers written on blackboard

Source: Argentina 1997 OMA L3 p4

5/13/2024
The first 19971997 natural numbers are written on the blackboard: 1,2,3,…,19971,2,3,\ldots ,1997. In front of each number, a "++" sign or a "−-" sign will be written in order, from left to right. To decide each sign, a coin is tossed; If it comes up heads, you write "++", if it comes up tails, you write "−-". Once the 19971997 signs are written, the algebraic sum of the expression on the blackboard is carried out and the result is SS. What is the probability that SS is greater than 00?
Clarification: The probability of an event is equal to the number of favorable cases/number of possible cases.
combinatorics