## Vineet Loomba is teaching live on Unacademy Plus

SOLVED PRACTICE PROBLEMS PROBABILITY JEE MAIN RANK BOOSTER COURSE PREPARED BY: ER. VINEET LOOMBA ITIAN IIT-JEE MENTOR

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ABOUT ME B.Tech. From IIT Roorkee -$ IIT-JEE Mentor Since 2010. Youtube Channel with 10k Active Followers & Founder @ vineetloomba.com * Follow me @ https://unacademy.com/user/vineetloomba to get unacademy updates or search me on Google * Share among your peers as SHARING is CARING!!

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Other Detailed Courses Made so far on Unacademv: V Strategy for JEE Main and Advanced V Sets, Relations and Functions V Trigonometry V Applications of Derivatives Limits, Continuity. Differentiability V Indefinite Integration Definite Integration Complex Number V Logarithmic Functions V Sequences Series V Most Important Questions in IIT-JEE Permutations Combinations Binomial Theorem V Straight Lines V Applications of Integrals MathematicS V Parabola (Detailed Course) v Inverse Trigonometry V Mathematical Reasoning V Ellipse (Detailed Course) V Hyperbola V Differential Equations Circles (Detailed Course) V Probability Upcoming Courses next month: Coordinate Geometry > Differential Equations ER. VINEET LOOMBA (IIT RooRKee) MATHEMATICS FOR IIT-I

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 3 EX. If P (A) , then find the odds against of A (A) 3 5 (B) 4 :5 (C) 3 : 4 (D) 5 : 3 PA)-8-PA)-1- .. odds in against of A - Sol, . PA). 5 PA)3 5.3 SUCCESS IN EE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. If the probability for A to fail in an examination is 0.2 and that of B to fail is 0.3, then the probability that either A or B fails is- (A) 0.5 (C) 0.56 Let A be event for A to fail and B be the event for B to fail, then P (A) 0.2 and P(B)0.3 Since A and B are independent events, .:. P (AB)P(A) P (B) :. Required probability (B) 0.44 (D) None of these Sol. = P(A+ B) P(A) P (B) P (AB) - P(A) P (B) P (A) P(B) - 0.2 0.3 0.2 x 0.3 0.5 0.06 0.44 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. If two dice are thrown together then what is the probability that the sum of their numbers is greater than 9. Sol. The sum of the numbers greater than 9 may be 10,11 and 12. If these events be A, B, C respectively, then P (A) 3/36 favourable cases are (6, 4), (5, 5), (4, 6)] P (B) = 2/36 [.. favourable cases are (6, 5), (5, 6)] P (C)1/36 [. favourable case is (6, 6)] Now since A, B, C are mutually exclusive, so P (A + B + C) = P(A) + P(B) + P (C) 3 2 1 36 36 36 6 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. Two cards are drawn one by one from a pack of 52 cards. If the first card is not replaced in the pack , then what is the probability that first card is that of a king and second card is that of a queen? (A) 4/664 (C) 6/663 (B) 5/663 (D) 4/663 So. Let A first card is that of a king Bsecond card is that of a queen 4 4 that P(A) - 5(BA) 5213 4 . P (AB) P (A) P (B/A) 13 51 663 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. One person can kill a bird twice in 3 shots, second once in 3 shots and third thrice in 4 shots. If they shot together then what is the probability that the bird will be killed? (A) 18/19 (C) 18/17 If A, B, C denote events of killing the bird by first second and third person respectively, then P (A) 2/3, P (B)1/3, P (C)3/4 The bird will be killed if atleast one of these three independent events happens. So Required probability (B) 17/18 (D) 20/17 Sol. -1-P/A 1) P (A2) P (Ag) -1-(1-2/3) (1-1/3) (1-34)-1-1/3. 2/3. 1/4-17/18 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Ex. A coin is tossed thrice. If E be the event of showing atleast two heads and F the event of showing head in the first throw, then P (E/F) is equal to- (A) 3/4 (B)3/8 (C) 1/2 There are following 8 outcomes of three throws: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT Also P (E F) = 3/8 and P (F) = 4/8 (D) 1/8 Sol. P (EnF) . required probability E/F)P ( 3/8 3 4/8 4 SUCCESS IN JEE MAIN AND ADVANCED ER. VINEET LOOMBA (IIT RooRKEE)

FOR 100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) ENROL for this Course (Free) Enroll 439 Recommend Lessons (Like) E Rate and Review the Course .Comments . Sharing with friends 15 1. 68 111 ratings 21 reviews Share ER. VINEET LOOMBA (IIT RooRKEE) MATHEMATICS FOR IIT-IEE