Conditional Probability

Probability of Class 12

Conditional Probability

Let S be the sample space. Let A and B be any events, A ≠ Φ. Then probability of the event B, assuming that A is known to have occurred, is called conditional probability of B restricted to the occurrence of A. It is denoted by P (B/A). Since A is assumed to have occurred, therefore, B occurs if and only if a sample point of B which is also in A results in (i.e. the event A ∩ B occurs). Thus probability of the event B restricted to the occurrence of the event A is the same as the probability of the event A ∩ B while A is considered as a sample space.

∴ PConditional Probability = = . From this it follows that  P(A ∩ B) = P(A).PConditional Probability.

If A ≠ Φ and B ≠ Φ, then P(A ∩ B) = P(A)PConditional Probability = P(B) P .

Talk to Our counsellor