for which of the following probability assignments are events a and b independent?

 It appears that you haven't provided the specific probability assignments or the events A and B for me to assess independence. In probability theory, events A and B are considered independent if the occurrence (or non-occurrence) of one does not affect the occurrence (or non-occurrence) of the other. Mathematically, this can be expressed as P(A and B) = P(A) * P(B).

If you provide the probability assignments or specific details about events A and B, I can help determine whether they are independent based on the given information

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