# Solutions of class 11 NCERT maths exercise 16.1 chapter 16 Probability

Solutions of class 11 NCERT maths exercise 16.1 chapter 16 Probability is based on fundamental rules of chapter 16. Here you can study the computation of different trials of an experiment. The set of different trials of an event or experiment is known as the sample space(S) of the experiment.All these NCERT solutions of class 11 NCERT maths exercise 16.1 chapter 16 Probability are very important for solving the problems on probability.

Solutions of class 11 NCERT maths exercise 16.1 chapter 16 Probability are created here by an expert of maths by a step by way, therefore we hope every student can understand them easily without facing any difficulties.

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**NCERT solutions of class 11 maths**

Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |

Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

Chapter 8- Binomial Theorem | Chapter 16- Probability |

**CBSE Class 11-Question paper of maths 2015**

**CBSE Class 11 – Second unit test of maths 2021 with solutions**

**Q1.Describe the sample space for the indicated experiment: A coin is tossed three times.**

Ans. A coin has two faces head(H) and tail (T)

In one toss there are two outcomes H and T

Therefore when the coin is tossed three-time it will have total outcomes =2³ = 8

Thus sample space for this experiment is = {(HHH),(TTT),(HHT),(TTH),(THH),(HTT),(HTH),(THT)}

**Q2.Describe the sample space for the indicated experiment: A die is thrown two times.**

Ans.A die has 6 faces corresponds to the digits 1,2,3,4,5,6

When a die is tossed once it has 6 outcomes 1.2.3.4.5.6 i.e =6

Therefore when the die is tossed two times it will have total outcomes =6² = 36

In set-builder form the sample space of total elements is written as ={(x,y): x,y = 1,2,3,4,5,6}

In roster form the sample space is written as following

{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

**Q3.Describe the sample space for the indicated experiment: A coin is tossed four times.**

Ans. A coin has two faces head(H) and tail (T)

In one toss there are two outcomes H and T

Therefore when the coin is tossed four times it will have total outcomes =2^{4 }= 16

Thus sample space for this experiment is = {(HHHH),(TTTT),(HHTT),(TTHH),(THHH),(HTTT),(HTTH),(THHT),(TTTH),(HTTT),(HTHT),(THTH),(HHTH),(TTHT)(HTHH),((THTT)}

**Q4.Describe the sample space for the indicated experiment: A coin is tossed and a die is thrown.**

Ans. A coin has two faces head(H) and tail (T)

In one toss there are two outcomes H and T

A die has 6 faces corresponds to the digits 1,2,3,4,5,6

When a die is tossed once it has 6 outcomes 1.2.3.4.5.6 i.e =6

If a coin is tossed and a die is thrown,then sample space of all elements is given by

S ={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

**Q5.Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.**

Ans. A coin has two faces head(H) and tail (T)

In one toss there are two outcomes H and T

A die has 6 faces corresponds to the digits 1,2,3,4,5,6

When a die is tossed once it has 6 outcomes 1.2.3.4.5.6 i.e =6

If a coin is tossed and a die is thrown in case a head is shown on the coin ,then sample space of all elements is given by

S ={H1,H2,H3,H4,H5,H6,T}

**Q6. Two boys and two girls are in room X and 1 boy and 3 girls in room Y. Spacify the sample space for the experiment in which a room is selected and then a person.**

Ans.There are two room X and Y

In first case let the two boys are represented by B1 and B2 and two girls are represented by G1 and G2, in second case 1 boy is represented by B3 and 3 girls are represented by G3,G4 and G5

In the given experiment we have to select first room and then a person,therefore the sample space of elements is given as

S ={XB1, XB2,XG1,XG2,YB3,YG3,YG4,YG5}

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**Q7.One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.**

Ans.Let red colour is denoted by R ,white colour is denoted by W and blue colour is represented by B

A die has 6 faces corresponds to the digits 1,2,3,4,5,6

When a die is tossed once it has 6 outcomes 1.2.3.4.5.6

According to the event, a die is first selected and then tossed, therefore the sample space is given as follows

S= {R1.R2.R3.R4.R5.R6 ,W1.W2.W3.W4.W5.W6 ,B1.B2.B3.B4.B5.B6 }

**Q8.An experiment consists of recording the boy-girl composition of families with 2 children.**

**(i) What is the sample space if we are interested in knowing whether it is a boy or a girl in the order of their birth.**

**(ii) What is the sample space if we are interested in the number of girls in the family.**

Ans. The experiment consists of a maximum of 2 children

Let the boy is represented by B and the girl is represented by G.

The sample space whether it is a boy or girls is given as follows

S = {BB,GG,BG,GB}

(ii) When the number of girls is considered as a outcome, since the experiment consists of a maximum of 2 children,therefore the results are of no girl,1 girl or 2 girls

S ={0,1,2}

**Q9.A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.**

Ans. There are 1 red and 3 white balls

Let red ball is represented by R and white ball is represented by W

Two balls are drawn at random, then the sample space is given by

S = {RW,WR,WW}

**Q10. An experiment consists of tossing a coin and then throwing it a second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.**

Ans. A coin has two faces head(H) and tail (T),when it is tossed once then outcomes are H,T

1 Coin is tossed second times if head occurs on first toss then the outcomes are HH,HT

A die has 6 faces corresponds to the digits 1,2,3,4,5,6

When a die is tossed once it has 6 outcomes 1.2.3.4.5.6

If a coin is tossed and tail occurs on the second toss, then a die is rolled once.,then sample space of all elements is given by {T1,T2,T3,T4,T5,T6}

Hence total sample space of the given experiment

S ={HH,HT,T1,T2,T3,T4,T5,T6}

**Q11.Suppose 3 bulbs are selected at random from a lot .Each bulb is tested and classified as defective (D) or non defective (N).Write the sample space of this experiment.**

Ans. 3 bulbs are tested and classified as defective (D) and non defective (N)

If 3 bulbs are selected at random from a lot,then sample space of this experiment is given by

S ={DDD,NNN,DDN,DND,NDD,NDN,NND,DNN}

**Q12.A coin is tossed .If the outcome is head ,a die is thrown,if the die shows up an even number,the die is thrown again. What is the sample space of this experiment.**

Ans. A coin has two faces head(H) and tail (T),when it is tossed once then outcomes are H,T

If the outcome is head on first toss then a die is thrown

When a die is tossed once it has 6 outcomes 1.2.3.4.5.6

if the die shows up an even number(2,4,6), then the die is thrown again,the outcomes should be H2, H4, H6 for throwing it again.

S= {H1, H3.H5,H21,H22, H23.H24.H25.H26,H41,H42, H43.H44.H45.H46,H61,H62, H63.H64.H65.H66,T}

**Q13. The numbers 1,2,3 and 4 are written on four slips of paper. The slips are put in a box and mix thoroughly. A person draws 2 slips from the box, one after the other, without replacement. Describe the sample space for this experiment.**

Ans. Since slip drawn is not to be replaced ,If first slip drawn is 1 then chances of second slip is of the numbers 2,3 or 4,so the outcomes are written as {(1,2),(1,3),(1,4)….., hence on the similar way the sample space for this experiment is written as follows.

S = {(1,2),(1,3),(1,4),(2,1),(2,3),(2,4),(3,1),(3,2),(3,4),(4,1),(4,2),(4,3)}

**Q14. An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.**

Ans.When a die is tossed once it has 6 outcomes 1.2.3.4.5.6

When a coin is tossed once then outcomes are H,T

A coin is tossed once if the number on the die is even(2,4,6)

A coin is tossed twiced if the number on the die is odd(1,3,5)

When a coin is tossed twiced then outcomes are HH,TT,HT,TH

Therefore sample space of this experiment is given as following.

S = {2H,2T,4H,4T,6H,6T,1HH,1TT,1HT,1TH,3HH,3TT,3HT,3TH,5HH,5TT,5HT,5TH}

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**NCERT Solutions for class 11 maths**

Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |

Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

Chapter 8- Binomial Theorem | Chapter 16- Probability |

**CBSE Class 11-Question paper of maths 2015**

**CBSE Class 11 – Second unit test of maths 2021 with solutions**

**NCERT solutions for class 12 maths**

Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

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