Explain conditional probability with the help of an example.

1.	Explain conditional probability with the help of an example.
Answer» Conditional Probability: Let A and B be two events associated with a random experiment. Then, the probability of the occurrence of A under the condition that B has already occurred and P(B) ≠ 0, is called the conditional probability of A given B and is written as P(A/B). Example: Suppose a red card is drawn from a pack of 52 cards, and is not put back, then the probability of drawing a red card in the first attempt is \(\frac{26}{52}\) and in the second one it is \(\frac{25}{51}\) as the red card is not replaced. Similarly in the above given case, if we draw a black card in the second attempt, then its probability = \(\frac{26}{51}\) as number of black cards = 26 but total number of remaining cards = 51. Hence the occurrence of the second event is fully dependent on the first event. Such events are called conditional events.

Answer»

Conditional Probability: Let A and B be two events associated with a random experiment. Then, the probability of the occurrence of A under the condition that B has already occurred and P(B) ≠ 0, is called the conditional probability of A given B and is written as P(A/B).

Example:

Suppose a red card is drawn from a pack of 52 cards, and is not put back, then the probability of drawing a red card in the first attempt is \(\frac{26}{52}\) and in the second one it is \(\frac{25}{51}\) as the red card is not replaced.

Similarly in the above given case, if we draw a black card in the second attempt, then its probability = \(\frac{26}{51}\) as number of black cards = 26 but total number of remaining cards = 51.

Hence the occurrence of the second event is fully dependent on the first event.

Such events are called conditional events.

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