## 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. * Doubts/Feedback in Comment Section *Comment other topics you want to revise . Follow me @https://unacademy.com/user/vineet! unacademy omba to get updates * Share among your peers as SHARING is CARING!! Search " vineet loomba unacademy" on GOOGLE

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Conditional Probability PAnB) P(B) If A and B are two events, then P(A/B) Note that for mutually exclusive events P(A/B)0 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solved Example: If P(A/B) 0.2 and P(B) 0.5 and P(A) 0.2. Find P(A nB) P(A B ) = P(A)-P(A B) Also P(A/B)= Solution. PAnB) From given data, P(A B)=0.1 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: Ifa pair of dice is thrown and it is known that sum of the numbers is even, then find the probability that the sum is less than 6. Solution: Let Abe the given event and let B be the event, whose probability is to be found Then Required probability P- PRAA) 1836 2 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Solved Example: If P(A) 0.25, P(B) 0.5 and P(An B) 0.14, find probability that neither A' nor 'B occurs. Also find P AnB) Solution We have to find P AnB1-P(AuB)(by De-Morgan's law) Also, P(Au B) P(A) + P(B)-PAnB) putting data we get, P AnB) 0.39 The shaded region denotes the simultaneous occurrence of Aand B Hence PAnB) PA)-PAB)-0.11 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Independent Events Two events A and B are said to be independent if occurrence or non-occurrence of one does not affect the occurrence or non-occurrence of the other, i.e., P(BA)-P(B), P(A)-0 P(B/A) = P(A) SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: In drawing two balls from a box containing 6 red and 4 white balls without replacement, Find if the following pairs is independent? (a)Red on first draw and red on second draw (b) Red on first draw and white on second draw Solution Let E be the event 'Red on first draw' F be the event 'Red on second draw' and G be the event 'white on second draw' 4 PE(F). P(G)1 6 6 SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 6P2 1 PEN F)=10P = 3 (a) E and F are not independent SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) 6 P(E) . P(G)=10 6 10-25 4 (b) 6P1 4P1 10p2 4 : 15 PENG) = . P(E) . P(G) P(E G) . E and G are not independent SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)