Let A and B be two events such that P(A∪B) = 1/6, P(A∩B) = 1/4 and P(¬A) = 1/4, where ¬A stands for the complement of the event A. Then the events A and B are:

Given P(A∪B) = 1/6, P(A∩B) = 1/4 and P(¬A) = 1/4

P(A) = 1 - P(¬A) = 1 - 1/4 = 3/4

P(A∪B) = P(A) + P(B) - P(A∩B)
1/6 = 3/4 + P(B) - 1/4
1/6 = 2/4 + P(B)
1/6 = 1/2 + P(B)
P(B) = 1/6 - 1/2 = 1/6 - 3/6 = -2/6 = -1/3
Since probability cannot be negative, there must be an error in the given probabilities. Let's assume the given probabilities are correct and proceed.

If A and B are independent, then P(A∩B) = P(A)P(B)
1/4 = (3/4) * P(B)
P(B) = 1/3

If A and B are equally likely, then P(A) = P(B)
3/4 = 1/3 (which is false)

Therefore, A and B are neither mutually exclusive nor independent, and they are not equally likely.
Let's re-examine the given probabilities. There's a high probability there's an error in the question statement since P(B) is negative which is impossible.