p. 1

conditional probability when we are solving conditional probability examples ,we deal with two events say a and b sometimes these events are so related to each other that the probability will depend on whether the other event has already occurred conditional probability can be defined as the probability of an event given that another event has already occurred let s consider an example for conditional probability consider a card game suppose a player needs to draw 2 cards of the same suit to win out of 52 cards there can be 13 cards in each suit if the first player draws a heart and the player wishes to draw a second heart if one heart has already been chosen then we only have 12 hearts remaining out of 51 cards so the conditional probability p 12/51 let us consider the random experiment of throwing a die let a be the event of getting an odd number on the die s {1 2 3 4 5 6 and a {1 3 5 let b {2 3 4 5 6 if after the die is thrown we are given the information that the event b has occurred then the probability of event a will no more be 1/2 because in this case the favourable cases are two and the total number of possible outcomes will be five and not six learn more about conditional probability

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p. 2

the probability of event a with the condition that event b has happened will 2/5 this conditional probability is denoted as pa/b let us define the concept of conditional probability in a formal manner let a and b be any two events associated with a random experiment the probability of occurrence of event a when the event b has already occurred is called the conditional probability of a when b is given and is denoted as pa/b the conditional probability pa/b is meaningful by definition pa/b probability of occurrence of event a when the event b as already occurred read more on probability and statistics

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p. 3

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