## 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 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)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Odds in Favour and Odds Against an Event As aresult of an experiment, if pof the outcomes are favourable to an event E and qofthe outcomes are against it, then we say that odds are p to q in favour of E or odds are q top against E number of number of unfavourable cases favourable cases p q and odds against an event Enumber of unfavourable cases Ifodds in favour of an event E arep: qthen the probability ofthe occurrence ofthat event is p+Q Similarly the probability of the non-occurrence ofthat eventis p+Q number of favourable cases p p+q SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: What are the odds in favour of throwing at least 8 in a single throw with two dice? Solution Let S be the sample space and E be the event of occurrence of a total of at least 8, then n(S)-6x 6-36 and n(E) = 15 15 P(E) = 36 15 21 36 36 Odds infavourofE P(E): P(E) 5:7] SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Self Practice Problem: What are the odds in favour of getting a spade if the card is drawn from a well-shuffled deck of cards? SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

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