Solutions

LM-C07-C-001

An unseen event has count 0. A plain count estimate assigns probability 0.

LM-C07-C-002

The middle count is 0 before smoothing. After add-one smoothing it becomes 1.

LM-C07-C-003

A 5-token vocabulary receives one extra count per token, so 5 count units are added.

LM-C07-C-004

0.7 + 0.3 = 1.

LM-C07-C-005

The path contains four orders: 4-gram, trigram, bigram, and unigram.