#pcfg

Question 1: Single choice

A PCFG has the rule $\mathrm{NP} \to \mathrm{DT}\ \mathrm{NN}\ \mathrm{NN}$ with probability 0.3. The CKY parser needs binary rules (Chomsky normal form). Using a new non-terminal $Z$ that appears nowhere else, which replacement keeps the probability of every parse tree unchanged?

$\mathrm{NP} \to \mathrm{DT}\ Z$ with 0.3, and $Z \to \mathrm{NN}\ \mathrm{NN}$ with 1.01
$\mathrm{NP} \to \mathrm{DT}\ Z$ with $\sqrt{0.3}$ , and $Z \to \mathrm{NN}\ \mathrm{NN}$ with $\sqrt{0.3}$ 2
$\mathrm{NP} \to \mathrm{DT}\ \mathrm{NN}$ with 0.3, and $\mathrm{NP} \to \mathrm{NN}\ \mathrm{NN}$ with 0.33
$\mathrm{NP} \to \mathrm{DT}\ Z$ with 0.3, and $Z \to \mathrm{NN}\ \mathrm{NN}$ with 0.34

Timed test