If A and B are mutually exclusive, then the union of A and B is simply their sums. Therefore p is half of 0.64, or 0.32.
If they are independent, then the odds of at least one of them occurring is 0.64. Therefore the odds of neither A nor B occurring is 1 - 0.64, or 0.36. Therefore 0.36 is (1-p)^2, so 1-p is 0.6, so p is 0.4. Sub that in to find k.
If they are independent, then the odds of at least one of them occurring is 0.64. Therefore the odds of neither A nor B occurring is 1 - 0.64, or 0.36. Therefore 0.36 is (1-p)^2, so 1-p is 0.6, so p is 0.4. Sub that in to find k.
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