Explanation
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(Aˉ)=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(A∪B)=61,P(A∩B)=41andP(A)=41
P(Aˉ)=1−P(A)=1−41=43
P(A∪B)=1−P(A∪B)=1−61=65
P(A∪B)=P(A)+P(B)−P(A∩B)
⇒P(B)=65−43+41=65−21=62
∴P(B)=31
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.
