first 1997 natural numbers written on blackboard
Source: Argentina 1997 OMA L3 p4
May 13, 2024
combinatorics
Problem Statement
The first natural numbers are written on the blackboard: . 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 signs are written, the algebraic sum of the expression on the blackboard is carried out and the result is . What is the probability that is greater than ?Clarification: The probability of an event is equal to the number of favorable cases/number of possible cases.