Could anyone show me the detailed explanation of this?

Thank you!

Let A and B be events that the S&P index and the DAX index close higher tomorrow respectively. Suppose that P(A) =0.4. Given that at least one of the events happens, there is a 1/3 chance that the S&P index closes lower tomorrow. Given that the DAX index closes lower tomorrow, there is a 1/5 chance that the S&P index closes higher tomorrow.

(a) Construct a probability table.

	A	A'	Total
B
B'
Total

(b) What is P(B|A)? Are the events A and B independent? Explain.