Concept: For any events A and B - P(A∪B)=P(A)+P(B)−P(A∩B) - Events are independent if P(A∩B)=P(A)×P(B) - Events are mutually exclusive if P(A∩B)=0 - P(A)=1−P(A) Calculation: Given P(A∪B)=
5
6
,P(A∩B)=
1
3
and P(A)=
1
2
P(A)=1−
1
2
=
1
2
P(A∪B)=P(A)+P(B)−P(A∩B)
5
6
=
1
2
+P(B)−
1
3
P(B)=
2
3
Given P(A∩B)≠0 P(A∩B)=P(A)×P(B)=
1
2
×
2
3
=
1
3
∴A and B are independent events and are not mutually exclusive events. Only statement 1 is correct.