Competition problem — Combinatorics

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Combinatorics Difficulty 4.4 AIME Find the answer United States

Problem:

At a nursery, $2006$ babies sit in a circle. Suddenly each baby pokes the baby immediately to either its left or its right, with equal probability. What is the expected number of unpoked babies?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

The probability that any given baby goes unpoked is $1/4$ . So the answer is $2006/4 = 1003/2$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.