## 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) 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) Example: A coin is tossed three times, consider the following events. A: 'No head appears', B: 'Exactly one head appears' and C: 'Atleast two heads appear Do they form a set of mutually exclusive and exhaustive events? Solution The sample space of the experiment is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} and A-(TTT), B {HTT, THT, TTH), C {HHT, HTH, THH, HHH) Now A u B u C = {TTT, HTT, THT, TTH, HHT, HTH, THH, HHH) = S Therefore, A, B and C are exhaustive events. Therefore, the events are pair-wise disjoint, ie, they are mutually exclusive. Hence, A, B and C form a set of mutually exclusive and exhaustive 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)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) PROBABILITY DEFINITION If an experiment results in a total of (m n) outcomes which are equally likely and mutually exclusive with one another and if 'm' outcomes are favorable to an event 'A while 'n' are unfavorable, then the probability of occurrence of the event 'A' denoted by numberof favourableoutcomes totalnumberof outcomes P(A) m + n SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: In throwing of a fair die find the probability of the event a number s 4 turns up' Sol: Sample space S . n(A)4 and n(S)6 1, 2, 3, 4, 5, 6); event A (1, 2, 3, 4) n(A) 4 2 P(A)S3 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: In throwing a pair of fair dice, find the probability of getting a total of 8 Sol. When a pair of dice is thrown the sample space consists (2, 6) Note that (1, 2) and (2, 1) are considered as separate points to make each outcome as equally likely To get a total of '8', favourable outcomes are, (2, 6) (3, 5) (4, 4) (5, 3) and (6, 2) Hence required probability- 36 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Six boys and six girls sit in a row randomly, find the probability that all the 6 girls sit together Sol: Let S be the sample space and E the event that all the 6 girls sit together n(S) -Total number of ways of seating 6 boys and 6 girls in a row 12! n(E)-number of ways of seating 6 boys and 6 girls in a row so that all the 6 girls sit together = 716! n(E) 6!7! 1 n(S) 12! 132 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example A four digit number is formed using the digits 0, 1, 2, 3, 4 without repetition. Find the probability that it is divisible by 4 Sol Total 4 digit numbers formed 4 4 3 2 9 Each of these 96 numbers are equally likely & mutually exclusive of each other Now, A number is divisible by 4, if last two digits of the number is divisible by 4 Hence we can haverst two places can be iled in 3 2 6 ways 12 two places can be filled in 2 x 2 4 ways 6 ways 4 ways 4 ways 6 ways 30 ways Total number of ways favorable outcomes probability Total outcomes 30- 96 Ans 16 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: In throwing of a fair die, find the probability of turning up of an odd number 24 Sol: S 11, 2, 3, 4, 5, 6) Let E be the event 'turning up of an odd number 2 4 then E (5) n (E) 1 . P(E) n (S) 6 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)