| GyanCentral - The hub for engineering and law students - IIT-JEE, AIEEE, BITSAT, CLAT, AILET - 2012: Probability for Clat Nov 27th 2012, 18:05 | GyanCentral - The hub for engineering and law students - IIT-JEE, AIEEE, BITSAT, CLAT, AILET - 2012 | | The source for all engineering and legal education news in India | | | Probability for Clat Nov 27th 2012, 17:09 Probability As the name suggests probability is the possibility of occurrence of any event. Probability (P) of an event may be calculated as Probability (P) = number of favourable outcomes/number of all possible outcomes There two events. One type of event is independent and has no direct connection among them which means that one event has no effect on the occurrence of the other event. For example tossing a coin and rolling a die together. Another event is such which are mutually exclusive event. There are two more rules which are similar to the rules of set theory. First is addition law which states that if X and Y are mutually exclusive event then probability that either event X or Y would occur in a single trial is P(X or Y)= P(X) + P(Y) If the events are not mutually exclusive then P(X or Y)= P(X) + P(Y) – P(X and Y together) Another rule is multiplication law which states that P(X and Y) = P(X) x P(Y) where x and y are independent events. Examples if a dice is thrown once then what is the probability of the number appearing on the top be 3 or more than that? S: No of favourable outcomes are: 3,4,5,6 so the number is 4. The number of possible outcomes are 6 as the dice as number from 1, 2, 3, 4, 5, 6. So as per the formula mentioned above the answer must be 4/6. A bag contains 6 red balls, 7 blue balls and 7 black balls. What is the probability that a ball drawn randomly be red or black? S: again the same formula will be used. We want to select one ball out of 20 so total outcome will be 20C1. Therefore total number of outcomes will be 20. No number of favourable outcomes is 6C1+7C1. The reason for using + sign between them is because of presence of OR in the question and the reason for using Combination is because we have to select from the given set of balls. Therefore the answer is 13/20. If two dice are thrown simultaneously then find the probability that the sum of numbers appearing on the top is less than or equal to 3? S: the total number of outcomes in this case is 36. This can be explained by (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2),…. The number on the left side include number on dice 1 and number on the right hand side of the ordered pair include number on the top of dice 2. Therefore in all 36 ordered pair will be formed. Number of favourable out comes will be (1, 2), (1,1) and (2,1). Therefore required probability will be 3/36 i.e. 1/12. Three cards are drawn at random from a pack of 52 cards. What is the probability of them being one jack, ace and king? S: three cards are selected in 52C3. Therefore total number of outcomes will be 22100. All the three jack, ace and king can be selected in 4C1. Total number of outcomes will be 4C1 X 4C1 X 4C1. . Note that multiplication sign is used because of AND present in the question. Therefore the ans is 64/22100 = 16/5525. |  | | |  |  |
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