# The Flower-Shop Intern

*English translation by SOTA – AI Community of the Russian original. Organisers who would like this translation removed can email sota.ai.community@gmail.com.*

*Task 2 of the school stage of the All-Russian School Olympiad (VsOSh) 2025/26 in artificial intelligence (region group III), grades 9–11. The official answer and solution are in a separate file.*

Customers of the flower delivery service “Monobouquet” order bouquets of roses with probability $\frac{2}{3}$ and bouquets of daisies with probability $\frac{1}{3}$. Yesterday the intern Petya carefully looked through the orders and sent out six bouquets: roses, roses, daisies, roses, roses, roses. After that, he decided not to waste time reading the descriptions, but to make all bouquets from roses only and send them straight to the customer's address. Today orders arrive one after another until a request for daisies appears; after that Petya will be fired, because the customer will receive the wrong bouquet! Find the mathematical expectation of the number of bouquets that Petya will manage to make correctly today.

**Scoring criterion:** 6 points for each correct answer. Total — 12 points

**Maximum score for the task — 12**