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

 It appears that the options for the probability assignments are missing from your question. In order to determine whether events A and B are independent, I would need the specific probabilities associated with each event or additional information about the events.

In probability theory, two events A and B are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the other event. Mathematically, for independent events A and B:

$�(�\cap �)=�(�)\cdot �(�)$

If you can provide the specific probability assignments or details about events A and B, I can help you determine their independence.