I have a doubt at the answer of the following problem:

Two spin-1/2 particles, 1 and 2, have spins in a singlet state with spin wave function

Ψ(1,2)=1/sqrt(2)[α(1) β(2) −α(2) β(1)]

where α and β refer to up and down spins, respectively, along any chosen axis. The spin of

particle 1 is measured along the z-axis and found to be up.

55. A simultaneous measurement of the spin of particle 2 along the z-axis would yield which of the

following results?

(A) Up with 100% probability

(B) Down with 100% probability

(C) Up with 25% probability, down with 75%

probability

(D) Up with 50% probability, down with 50%

probability

(E) Up with 75% probability, down with 25%

probability

The answer is "D", but my answer is "B". Because I think this is a quantum entanglement state, when the spin of particle "1" is measured, the state of particle "2" is completely assured. It must be "Down".