AMC 12 2025 Part B Problem 18

Awnik repeatedly plays a game that has a probability of winning of \dfrac{1}{3}. The outcomes are independent. What is the expected value of the number of games he will play until he has both won and lost at least once?

Answer Choices:

A. \dfrac{5}{2}

B. 3

C. \dfrac{16}{5}

D. \dfrac{7}{2}

E. \dfrac{15}{4}