What do you think the chances are of them coming?
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Gleb_ChebrikoffWhat are the chances of them coming?
Therefore, we may look upon as a special type of insert that should not interfere with the positioning of the operator. In other words:
What do you think are the chances of them coming?
I disagree. If that was true, then the following reasoning would be alright:
What do I need? ---> What do