AMC 12A 2025 (Problem 22)

Three real numbers are chosen independently and uniformly at random between

0

and

1

. What is the probability that the greatest of these three numbers is greater than

2

times each of the other two numbers? (In other words, if the chosen numbers are

a\ge b\ge c

, then

a>2b

\text{(A)}\;\frac{1}{12}

\text{(B)}\;\frac{1}{9}

\text{(C)}\;\frac{1}{8}

\text{(D)}\;\frac{1}{6}

\text{(E)}\;\frac{1}{4}