P(B/A) is defined only whena)A is a sure eventb)B is a sure eventc)A i...
Definition of P(B/A)
P(B/A) is the conditional probability of event B occurring given that event A has already occurred. It is denoted by P(B|A) and is given by the formula:
P(B|A) = P(A and B) / P(A)
where P(A and B) is the probability of both events A and B occurring together, and P(A) is the probability of event A occurring.
Conditions for P(B/A) to be defined
To calculate the conditional probability P(B/A), certain conditions need to be met. These conditions are as follows:
A is not an impossible event
Event A must have a non-zero probability of occurring. If event A has a probability of zero, then it cannot occur, and hence, the conditional probability P(B/A) is undefined.
B is not an impossible event
Event B must also have a non-zero probability of occurring. If event B has a probability of zero, then it cannot occur, and hence, the conditional probability P(B/A) is undefined.
A is a sure event
If event A is a sure event, i.e., it is certain to occur, then the conditional probability P(B/A) is defined for any event B, regardless of its probability of occurrence.
B is a sure event
If event B is a sure event, i.e., it is certain to occur, then the conditional probability P(B/A) is defined for any event A, regardless of its probability of occurrence.
Conclusion
Therefore, the correct answer is option C, i.e., P(B/A) is defined only when A is not an impossible event. This is because if event A has a probability of zero, then it cannot occur, and hence, the conditional probability P(B/A) is undefined.
P(B/A) is defined only whena)A is a sure eventb)B is a sure eventc)A i...
P(B/A)=P(
A⋂B)/P(A) . If A is impossible event , P(A)=0 Then P(B/A) will be undefined . so A should not be Impossible event.