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Class 12-science RD SHARMA Solutions Maths Chapter 33: Binomial Distribution

Binomial Distribution Exercise Ex. 33.1

Solution 1


Solution 2

Solution 3

Solution 4


Solution 5

Solution 6

Solution 7

Solution 8

Required Probability =4547 over 8192

Solution 9

Solution 10

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Solution 12


Solution 13


Solution 14

Solution 15

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Solution 17



Solution 18

Solution 19

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Solution 21



Solution 22


Solution 23



Solution 24



Solution 25



Solution 26


Solution 27

Solution 28

Solution 29


Solution 30

Solution 31

Solution 32


Solution 33

                                = 0.0256

Solution 34


Solution 35

Solution 36


Solution 37

Solution 38

Solution 39

Solution 40

Solution 41

Solution 42

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Solution 45

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Solution 47

Solution 48

Solution 49

Solution 50

  

Solution 51

  

Solution 52

  

Solution 53

  

Note: Answer given in the book is incorrect.

Binomial Distribution Exercise Ex. 33.2

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Solution 6


Solution 7

Solution 8

Solution 9

Solution 10

Solution 11


Solution 12

Solution 13

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Solution 15

Solution 16

Solution 17

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Solution 19

Solution 20

Solution 21

Solution 22

Out of 15 bulbs 5 are defective.

 

begin mathsize 12px style table attributes columnalign left end attributes row cell text Hence ,  the   probability   that   the   drawn   bulb   is   defective   is end text end cell row cell text P end text left parenthesis text Defective end text right parenthesis equals 5 over 15 equals 1 third end cell row cell text P end text left parenthesis text Not   defective end text right parenthesis equals 10 over 15 equals 2 over 3 end cell row cell text Let   X   denote   the   number   of   defective   bulbs   out   of   4. end text end cell row cell text Then ,  X   follows   binomial   distribution   with   end text end cell row cell straight n equals 4 comma text   end text straight p equals 1 third text   and   end text straight q equals 2 over 3 text   such   that end text end cell row cell straight P left parenthesis straight X equals straight r right parenthesis equals straight C presuperscript 4 subscript straight r open parentheses 1 third close parentheses to the power of straight r open parentheses 2 over 3 close parentheses to the power of 4 minus straight r end exponent semicolon straight r equals 0 comma 1 comma 2 comma 3 comma 4 end cell row cell text Mean end text equals sum from straight r equals 0 to 4 of rP left parenthesis straight r right parenthesis equals 1 cross times straight C presuperscript 4 subscript 1 open parentheses 1 third close parentheses open parentheses 2 over 3 close parentheses cubed plus 2 cross times straight C presuperscript 4 subscript 2 open parentheses 1 third close parentheses squared open parentheses 2 over 3 close parentheses squared end cell row cell plus 3 cross times straight C presuperscript 4 subscript 3 open parentheses 1 third close parentheses cubed open parentheses 2 over 3 close parentheses plus 4 cross times straight C presuperscript 4 subscript 4 open parentheses 1 third close parentheses to the power of 4 open parentheses 2 over 3 close parentheses to the power of 0 end cell row cell equals 32 over 81 plus 48 over 81 plus 24 over 81 plus 4 over 81 equals 108 over 81 equals 4 over 3 end cell end table end style

Solution 23

  

Solution 24

  

Solution 25

  

Binomial Distribution Exercise MCQ

Solution 1

Correct option: (a)

  

Solution 2

Correct option: (b)

  

Solution 3

Correct option: (c)

  

Solution 4

Correct option: (c)

  

Solution 5

Correct option: (a)

  

Solution 6

Correct option: (c)

  

 

Solution 7

Correct option: (a)

  

Solution 8

Correct option: (a)

  

Solution 9

Correct option: (b)

  

 

Solution 10

Correct option: (a)

  

Solution 11

Correct option: (d)

  

Solution 12

Correct option: (d)

  

Solution 13

Correct option: (a)

  

Solution 14

Correct option: (b)

  

Solution 15

Correct option: (c)

  

Solution 16

Correct option: (b)

  

Solution 17

Correct option: (d)

  

Solution 18

Correct option: (d)

 

NOTE: Answer not matching with back answer.

Solution 19

Correct option: (b)

  

Solution 20

Correct option: (b)

  

Solution 21

Correct option: (c)

  

Solution 22

Correct option: (d)

  

Solution 23

 

NOTE: Answer not matching with back answer.

Solution 24

Correct option: (b)

  

Solution 25

Correct option: (d)

  

Solution 26

Correct option: (d)

  

Solution 27

Correct option: (a)

  

Solution 28

Correct option: (a)

  

Solution 29

Correct option: (c)

In Binomial distribution trails are independent.

Solution 30

Correct option: (b)

  

Binomial Distribution Exercise Ex. 33VSAQ

Solution 1

Solution 2

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Solution 4

Solution 5

rightwards double arrow q equals 0.4

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Solution 9

Solution 10