## 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) 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)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: IfA andB are independent events. Then show that the following pairs of events are also independent (i) A' andB(ii) A' and B' Solution O P(A'B)-P(B)-P(AnB) P(B)-P(A)P(B) (: A and B are independent) -P(B) ( PA))-P(B) P(A) -1-P(A)-P(B)+ P(A). P(B) (1-PA))PB) P(A). P(B) SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: A speaks truth in 60% of the cases and b in 90% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact? Solutiorn Let E be the event that A speaks truth and F be the event that B speaks truth. Then E and F are independent events such that 60 3 100 5 909 100 10 P(E) = and P(F)= = A and B will contradict each other in the following ways () A speaks truth and B tells a lie i.e. En F () A tells a lie and B speaks truth lie i.e. EF P(A and B contradict each other) -P(E F)+ P (E nF) P(E) P(F) + P(E)P(F) [ EnF and E F are mutually exclusive] [: E and F are in dep.] 3 9 3 2 9 21 510 5 10 5 10 50 x10 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: A box contains 5 bulbs of which two are defective. Test is carried on bulbs one by one untill the two defective bulbs are found out. Find the probability that the process stops after (0)Second test Solution (C)Process will stop after second test, Only if the first and second bulb are both found to be defective (i) Third test probability - 5 10 (i) Process will stop after third test when either (a) DND > or(b) NDD or(c) NNN 5 4 3 10 5 4 3 10 hence required probability = 5 4 3 10 SUCCESS IN EE MAIN ER. VINEET LOOMBA (IIT RooRKEe)

100% SUCCESS IN JEE MAIN AND ADVANCED (IIT-JEE) Example: If cards are drawn one by one from a well shuffled pack of 52 cards without replacement, until an ace appears, find the probability that the fourth card is the first ace to appear. Solution 'NN NA is the arrangement than we de sire in taking out cards, one by one 48 47 46 4 49 Hence required chance is SUCCESS IN JEE MAIN ER. VINEET LOOMBA (IIT RooRKEE)