AMC 10A 2026 (Problem 12)

A drawer has 100 red socks and 100 blue socks. Pippi randomly removes one sock at a time, without replacement, until all the socks of one color have been removed. What is the probability that there are exactly 2 socks left in the drawer once that happens?

\text{(A)}\;\frac{27}{196}

\text{(B)}\;\frac{49}{198}

\text{(C)}\;\frac{247}{990}

\text{(D)}\;\frac{50}{199}

\text{(E)}\;\frac{25}{99}