What is conditional probability. explain with an example.

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Explain conditional probability with the help of an example.

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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.