NDA Math Probability Part 2

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.