Concept:

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

The probability of the complement of an event is one minus the probability of the event. P (A̅) = 1 - P (A)

To determine the probability of two independent events, we multiply the probability of the first event by the probability of the second event. P(A ∩ B) = P(A)·P(B)

Two events are mutually exclusive when two events cannot happen at the same time. P(A ∩ B) = 0

In equally likely events, the probabilities of each event are equal.

Calculation:

Here, \( P(\overline{A \cup B}) = \dfrac{1}{6}, P(A \cap B) = \dfrac{1}{4} \, \text{and} \, P(\overline{A}) = \dfrac{1}{4} \)

P(A) = 1 - P(A̅) = 1 - 1/4 = 3/4

\( \text{P}(A \cup B) = 1 - P(\overline{A \cup B}) = 1 - \dfrac{1}{6} = \dfrac{5}{6} \)

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

⇒ P(B) = 5/6 - 3/4 + 1/4 = 5/6 - 1/2 

= 2/6

P(B) = 1/3

Here, P(A ∩ B) = P(A)·P(B) and P(A) ≠ P(B), so the events are independent but not equally likely.

Hence, option (1) is correct.