Answer:
A. 1. P(A∪B)=0.85
2. P(A∩C)=0.045
3. P(A/B)=0.3
4. P(B∪C)=0.70
B. Event B and Event C are dependent
Step-by-step explanation:
A. As events are mutually exclusive, so,
P(A∪B)=P(A)+P(B)
P(A∩B)=P(A)*P(B)
1. P(A∪B)=?
P(A∪B)=P(A)+P(B)=0.3+0.55=0.85
P(A∪B)=0.85
2. P(A∩C)
P(A∩C)=P(A)*P(C)=0.30*0.15=0.045
P(A∩C)=0.045
3. P(A/B)
P(A/B)=P(A∩B)/P(B)
P(A∩B)=P(A)*P(B)=0.30*0.55=0.165
P(A/B)=P(A∩B)/P(B)=0.165/0.55=0.3
P(A/B)=0.3
4. P(B∪C)
P(B∪C)=P(B)+P(C)=0.55+0.15=0.70
P(B∪C)=0.70
B.
The event B and C are mutually exclusive and events B and event C are dependent i.e. P(B and C)≠P(B)P(C)
The events are mutually exclusive i.e. P(B and C)=0
whereas P(B)*P(C)=0.55*0.15=0.0825
Mutually exclusive events are independent only if either one of two or both events has zero probability of occurring.
Thus, event B and C are dependent
