How to generate text 7 states:

Beam search will always find an output sequence with higher probability than greedy search

It’s not clear to me why that is the case. Consider this example, comparing greedy search with beam search with beam width 2:
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By the 3rd step, beam search with beam width 2 has found two sequences BFI and BGK, each with probability .49*.5*.51 = 0.12495, but greedy search found ADH, with probability .51*.4*.99 = 0.20196
Exploring more of the tree may cause beam search to get stuck on paths that seem more promising at first, but end up with lower probability than the greedy path. Is this right, or have I misunderstood how beam search works?
Thanks!
Robby