Suppose that the probability that the price of a commodity goes up today is 0.6 that the probability that it goes up tomorrow is 0.7, and that the probability it goes up both today and tomorrow is 0.5. Find the probability that it goes down or remains the same both today and tomorrow.
Let A =the price goes up today and B=price goes up tomorrow.
we have P(A)=0.6, P(B)=0.7, P(AandB)=0.5
Do they want 1-P(AandB)=0.5?
Yes, if you think of the commodity price change on a number line... it going up would be (>), the only other 2 possibilities for it would be going down (<) or remaining the same (=).
So if C = the price goes down today, D = the price goes down tomorrow,
and E = the price stays the same today, F = the price stays the same tomorrow.
Then the probability that the prices go down *or* remain the same today *and* tomorrow is : P((C or E) and (D or F))
P((C or E) and (D or F)) = P(NOT(A and B))
= 1 - P(A and B)
= 1 - 0.5