## Vineet Loomba is teaching live on Unacademy Plus

PROBABILITY FoR SURe SHoT SUcCESS IN JEE MAIN AND ADVANCED (IIT-JEE) JEE MAIN RANK BOOSTER COURSE PREPARED BY ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) SPECIAL ANNOUNCEMENT Share useful links and advice with your learners... CRASH COURSE FOR JEE MAIN 2019 (JANUARY SESSION) Find courses & lessons 735 Courses IIT JEE 2,521 Courses Str Chemistry 797 Courses Details in Plus Tab wwEest HINDI Home My Library Plus Profile SUCCESS IN JEE MAIN ER. VINEET LoOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B. Tech. From IIT Roorkee IIT-JEE Mentor Since 2010. * Many of my students are pursuing courses in IITs, NITs, BITs etc unacademy Currently running my own Coaching Institute for JEE Main and Advanced Search vineet loomba unacademy on GOOGLE

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) (i) Random Experiment : It is a process which results in an outcome which is one of the various possible outcomes that are known to us before hand (ii) Sample Space : It is the set of all possible outcomes of a random experiment SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solved Example: Write the sample space of the experiment 'A coin is tossed, if it shows head a coin tossed again else a die is thrown Solution: The sample space S = {HH, HT, TI, T2, T3, T4, T5, T6) SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solved Example # 3 Find the sample space associated with the experiment of rolling a pair of dice once 2 4 6 2 4 (4,1 (4, 2) 4, 3) 4,4) (4,5) (4, 6) 5 (5,1) 5, 2) 5,3) (5,4) (5,5) (5, 6) 6 6,1) 6,2) 6,3) 6,4) 6,5) (6, 6) SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Sample Point Each element of the sample space is called a sample point. Event An event is a subset of the sample space. When a die is rolled, sample space is S -1,2, 3, 4, 5, 6 Let A 1,3, 5), B- 2, 4, 6,, C 1, 2, 3, 4 A: Event of occurrence of an odd number, B: Event of occurrence of an even number C Event of occurrence of a number less than 5. SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Simple Event An event is called a simple event, if it is a singleton subset of the sample space S Compound Event A subset of the sample space S which contains more than one element is called a compound event Equally likely Events If events have same chance of occurrence, then they are said to be equally likely SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solved Example: Write down all the events of the experiment 'tossing of a coin'. Solution: S = {H, T} the events are f , {B), {T) (H T) SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Mutually Exclusive or Disjoint Events: Two events are said to be mutually exclusive if occurrence of one of them rejects the possibility of occurrence of the other i.e. both cannot occur simultaneously e.g. In throw of a dice A- occurrence or even numbers and B-Occurrence of odd numbers SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Exhaustive Events A system of events is said to be exhaustive if on each performance of the experiment at least one of the events of the system is must to occur. In set theoretic notation, events Ai, Ar . . . , Amare exhauster UAp5 . i-1 For example on throwing of a die, the events 1,2), (2,3,4), 5) and (4, 5, 63 form an exhaustive system of events. SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment A: 'the sum is even' C: the sum is less than 4. Which pairs of these events are mutually exclusive? B: "the sum is a multiple of 3. D: 'the sum is greater than Solution There are 36 elements in the sample space S {(, y): x, y 1, 2, 3, 4, 5,6) D (6, 6)) A n B-{(1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6)) The pairs (A, C), (A, D), (B, C), (B, D) are not mutually exclusive events But C n D , so C and D are mutually exclusive events SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)