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

 I'm sorry, but it seems like the list of probability assignments and events A and B is not provided in your question. To determine whether events A and B are independent, you typically need information about the probability of each event and the joint probability (probability of both events occurring together).

The mathematical definition of independent events is that the occurrence or non-occurrence of one event does not affect the occurrence or non-occurrence of the other. In terms of probability, this can be expressed as:

�(�∩�)=�(�)⋅�(�)

If this equality holds, then events A and B are independent. If not, they are dependent.

If you can provide the specific probability assignments or details about events A and B, I would be happy to help you determine whether they are independent or not

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