## Jagat Chaudhary is teaching live on Unacademy Plus

IIT-JEE (main +Advanced) Probability On

dependent Events.

t Sndependent Events: Tuoo events A and are said o be independent f occurance or mo occurance of one, doesnot affect the probabil, of occurance or non ocurone of othes

3ndependent Events. Tuoo events A and are said to be independent If ccurance mon occurance of one , doesn affect the probabil f occuvante ar nnotcuvane A cain 1s tossed and a dice is rolled then nd Padoabili of g Example is bo etinq Head on Coinand 6 on dice P on dice and Head on coin

Ondebendent Event s Tuo events A and B a e said -to be independent occurance of one, doesnot affect the probabi li of othes. coin 1s tossed and a dice is olled then Bnd Parbabiliy of g ethng Head on Coinand 6 on dice e PL Con dice and Head on coin Sample space I 2 3 4 5 2H, T

Ondebendent Event s Tuoo events A anel are said to be independent occurance of one, doesnot broba bi ),.ty of occura ne nona CC UzqnQ of othe. Examble A coin is tossed and a di ce is rolled -hen find of getting Head on coin and 6 on dice e PL Con dice and Head on coin bil i Sample space I 2 3 4 5 3H, BT 6H , 6T 2

Ondebendent Events Tuco even A and B a e said t be independent occurance of one, doesnot affect the probabi li of othe. Example A coin s tossed and a dice is ol Padoabili of getting Head ed then Bnd on Coin and 6 on dice e PL Con dice and Head on coin Sample space 2 3 4 2H, T 3H, BT 5 5H , ST 18 2 = p(A) P(B)

ndependent Events: Too even A and B a e said to be independent occurance of one, doesnot affect the probabi li of othe. coin 1s tossed and a dice is olled then Bnd Porbabiliy of gethng Head on Coin and 6 on dice 'e PL Con dice and Head on coin Sample space 2 3 4 5 3H, BT 5H , ST la 2 =f(A) PLB) oo-ther exam ble PC H amol and and flood)

ndependent Events: Too even A and B a e said to be independent occurance of one, doesnot affect the probabi li of othe. coin 1s tossed and a dice is olled then Bnd Porbabiliy of gethng Head on Coin and 6 on dice 'e PL Con dice and Head on coin Sample space 2 3 4 5 3H, BT 5H , ST la 2 =f(A) PLB) oo-ther exam ble PL H and 6 and and flood) =

ndependent Events: Too even A and B a e said to be independent occurance of one, doesnot affect the probabi li of othe. coin 1s tossed and a dice is olled then Bnd podoabili of gethng Head on coin and 6on dice 'e PL Con dice and Head on coin Sample space 2 3 4 5 3H, BT 5H , ST 2 =f(A) PLB) oo-ther exam ble PL H and 6 and m and flood) =

ndependent Events: Too even A and B a e said to be independent occurance of one, doesnot affect the probabi li of othe. coin 1s tossed and a dice is olled then Bnd Porbabiliy of gethng Head on Coin and 6 on dice Example A 'e PL Con dice and Head on coin Sample space 2 3 4 5 3H, BT 4H, 4T 5H , ST la 2 oo-ther exam ble PL H and 6 and m and flood) = x T15

ndependent Events: Too even A and B a e said to be independent occurance of one, doesnot affect the probabi li of othe. coin 1s tossed and a dice is olled then Bnd Porbabiliy of gethng Head on Coin and 6 on dice Example A 'e PL Con dice and Head on coin Sample space 2 3 4 5 3H, BT 5H , ST 2 oo-ther exam ble PL H and 6 and nm and flood) = x T15 5oo

xample, 9f we had loo toss es in loo thzouws of a Coin The babiigethrg Head en lalth toss 2

b,S thnv are drawn on the table.F Ques:A purse contain 10 tickets. 5 printed with I, 5 Printed with T. 3 tickets are drawn without replacement and arranged in same order, in which they are drawn on the table. Find the probability that (1) IIT is formed.

Ques: From an urn containing 2 Red, 3 Green and 5 White balls. 3 Balls are drawn. (1) What is the probability that balls drawn in sequence of Red, Green and White.

Ques: From an urn containing 2 Red, 3 Green and 5 White balls. 3 Balls are drawn. (1) What is the probability that balls drawn in sequence of Red, Green and White. Answer-10 ^ 8 (without replacement)

Ques: From an urn containing 2 Red, 3 Green and 5 White balls. 3 Balls are drawn. (1) What is the probability that balls drawn in sequence of Red, Green and White. Answer-10 ^ 8 (without replacement) Answer- i-.^.^ (Replacement) r= 10.3 .10 (Replacement) 10 10 10

(2) A Ball drawn and is observed and put back again in urn, find probability that balls are of different colours

ueso mtra mmbers ase selecled om st uwenty malural mumbes. Find the boobabi Their sum is odd A- 11,2,3,4, - -,2o

QueSnatural mumbers ae selected ms twenty matural mmbers. Find the bobabi O Ther sum is odd A-1,2,3, 4,- ,2o Sum odd is bossible F one no. is even and one odd Poobabibt- orlo 2 C2

QueSnatural mumbers ae selected m s tuwenty maural umbers. Find he pobabil O Ther sum is odd A ,2, 3, 4, - --,2o Sum odd is possible if one mo. is even and one odd PrDbabili orlo 2 20 C2 (2 Sum i Even 1-PLodd) P Even Som) PC Even Sonn)- 4 19

10 apples are distributed at random among 6 persons. The probability that at least one of them will receive none, is 14 6 a) c) 137 143 d) None of these 143 15 C 5 Write answer in comment box unacademy LIVE Jagat Chaudhary Follow Qualified IIT-JEE,JITJAM. Expert faculty for IIT-JEE Mathematics Courses. M.Sc. Ph.D. (MATHEMATICS) IIT Bhubaneswar.Cofounder at Aspiration