The question is incomplete. Below you will find the missing contents.
The correct match of events with order are,
- P(A)P(B|A) - Dependent event
- P(A)+P(B) - Mutually exclusive events
- P(A and B)/P(A) - Conditional events
- P(A) . P(B) - Independent Events
- P(A)+P(B) -P(A and B) - not Mutually exclusive events.
When two events A and B are independent then,
P(A and B)=P(A).P(B)
when A and B are dependent events then,
P(A and B) = P(A) . P(B|A)
When two events A and B are mutually exclusive events then,
P(A and B)=0
So, P(A or B) = P(A) + P(B) - P(A and B) = P(A) + P(B)
P(A) + P(B) = P(A or B)
When events are not mutually exclusive then the general relation is,
P(A or B) = P(A) + P(B) - P(A and B)
If the probability of the event B conditioned by A is given by,
[tex]\mathrm{P(B|A)=\frac{P(A~and~B)}{P(A)}}[/tex]
Hence the correct match are -
- [tex]\mathrm{P(A)P(B|A)\rightarrow}[/tex] Dependent event
- [tex]\mathrm{P(A)+P(B)}\rightarrow[/tex] Mutually exclusive events
- [tex]\mathrm{\frac{P(A ~and ~B)}{P(A)}\rightarrow}[/tex] Conditional events
- [tex]\mathrm{P(A) . P(B)\rightarrow}[/tex] Independent Events
- [tex]\mathrm{P(A)+P(B) -P(A ~and ~B)\rightarrow}[/tex] not Mutually exclusive events.
Learn more about Probability of Events here -
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