Probability Problems 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. Letâ&#x20AC;&#x2122;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 Know More About Slope Formulas

Let us consider the random experiment of throwing a die. Let A be the event of getting an odd number on the die. 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. The probability of event A, with the condition that event B has happened will 2/5. This conditional probability is denoted as P(A/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 P(A/B). The conditional probability P(A/B) is meaningful So far, we have assumed that the elementary events are equally likely and we have used the corresponding definition of probability. However the same definition of conditional probability can also be used when the elementary events are not equally likely. This will be clear from the following example. Suppose a die is tossed. Let B be the event of getting a perfect square. Learn More On :- What is the Formula for Slope

The die is so constructed that the event numbers are twice as likely to occur as the odd numbers. Let us find the probability of B given A, where A is the event getting a number greater than 3 while tossing the die.

Conditional Probability Examples Example 1 :- A card is drawn from an ordinary deck and we are told that it is red, what is the probability that the card is greater than 2 but less than 9. Solution :- Let A be the event of getting a card greater than 2 but less than 9. B be the event of getting a red card. We have to find the probability of A given that B has occurred. That is, we have to find P (A/B). In a deck of cards, there are 26 red cards and 26 black cards. \ n(B) = 26 Among the red cards, the number of outcomes which are favourable

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