NCERT Solutions for Exercise 16.1 Class 11 Maths Chapter 16 - Probability

NCERT Solutions for Exercise 16.1 Class 11 Maths Chapter 16 - Probability

Edited By Ravindra Pindel | Updated on Jul 12, 2022 04:37 PM IST

In previous classes, you have already learned about probability defined as a mathematical measurement of the uncertainty of any phenomena. In exercise 16.1 Class 11 Maths, you will come across two terms namely outcomes and sample space. The outcome in any experiment is a possible result of a random experiment and the sample space of an experiment is defined as the set of all possible outcomes of a random experiment.

In NCERT solutions for Class 11 Maths Chapter 16 exercise 16.1, you will get questions related to finding sample space for the given experiment. You can try to solve these questions given in the Class 11 Maths chapter 16 exercise 16.1 in order to get more clarity. Conceptual clarity of these concepts is very important to understand upcoming exercises. Also, if you are looking for NCERT Solutions at one place, you can visit the given link.

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Question:1 Describe the sample space for the indicated experiment.

A coin is tossed three times.

Answer:

Let H denote Heads and T denote Tails.

For each toss, there are two possible outcomes = H or T

The required sample space is:

S = {HHH, HHT, HTH, THH, TTH, HTT, THT, TTT}

A die is thrown two times.

Answer:

When a die is thrown, the possible outcomes are = {1, 2, 3 ,4 ,5 ,6}

The required sample space is:

S = { $\dpi{100} (x, y) : x, y$ = 1,2,3,4,5,6}

or S = {(1,1), (1,2), (1,3), ..., (1,6), (2,1), (2,2), ..., (2,6), ..., (6, 1), (6, 2), ..., (6,6)}

A coin is tossed four times.

Answer:

Let H denote Heads and T denote Tails.

For each toss, there are two possible outcomes = H or T

The required sample space is:

S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT}

A coin is tossed and a die is thrown.

Answer:

Let H denote Heads and T denote Tails.

For each toss, there are two possible outcomes = H or T

And,

When a die is thrown, the possible outcomes are = {1, 2, 3 ,4 ,5 ,6}

The required sample space is:

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

A coin is tossed and then a die is rolled only in case a head is shown on the coin.

Answer:

Let H denote Heads and T denote Tails.

For each toss, there are two possible outcomes = H or T

For H, when a die is thrown, the possible outcomes are = {1, 2, 3 ,4 ,5 ,6}

The required sample space is:

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

2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.

Answer:

Let X denote the event Room X is selected, Y denote the event Room Y is selected.

B1, B2 denote the event a boy is selected and G1, G2 denote the event a girl is selected from room X.

B3 denotes the event a boy is selected and G3, G4, G5 denote the event a girl is selected from Room Y.

The required sample space is:

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

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.

Answer:

Let, R denote the event the red die comes out,

W denote the event the white die comes out,

B denote the event the Blue die is chosen

When a die is thrown, the possible outcomes are = {1, 2, 3 ,4 ,5 ,6}

The required sample space is:

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

What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

Answer:

Let B denote the event a boy is born,

G denote the event a girl is born

The required sample space with a boy or girl in the order of their births is:

S = {BB, BG, GB, GG}

What is the sample space if we are interested in the number of girls in the family?

Answer:

(ii) In a family with two child, there can be only three possible cases:

no girl child, 1 girl child or 2 girl child

The required sample is:

S = {0, 1, 2}

Answer:

Given, Number of red balls =1

Number of white balls = 3

Let R denote the event that the red ball is drawn.

And W denotes the event that a white ball is drawn.

Since two balls are drawn at random in succession without replacement,

if the first ball is red, the second ball will be white. And if the first ball is white, second can be either of red and white

The required sample space is:

S = {RW, WR, WW}

Answer:

Let H denote the event that Head occurs and T denote the event that Tail occurs.

For T in first toss, the possible outcomes when a die is thrown = {1, 2, 3 ,4 ,5 ,6}

The required sample space is :

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

Answer:

Let D denote the event the bulb is defective and N denote the event the bulb is non-defective
The required sample space is:

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

Answer:

Possible outcomes when a coin is tossed = {H,T}

Possible outcomes when a die is thrown = {1,2,3,4,5,6}

When T occurs, experiment is finished. S1 = {T}

When H occurs, a die is thrown.

If the outcome is odd ({1,3,5}), S2 = {H1, H3, H5}

If the outcome is even({2,4,6}), the die is thrown again.,

S3 = {H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66}

The required sample space is:

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

Answer:

Given, two slips are drawn from the box, one after the other, without replacement.

Let 1, 2, 3, 4 denote the event that 1, 2, 3, 4 numbered slip is drawn respectively.

When two slips are drawn without replacement, the first event has 4 possible outcomes and the second event has 3 possible outcomes

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)}

Answer:

Possible outcomes when a die is thrown = {1,2,3,4,5,6}

Possible outcomes when a coin is tossed = {H,T}

If the number on the die is even {2,4,6}, the coin is tossed once.

S1 = {2H, 2T, 4H, 4T, 6H, 6T}

If the number on the die is odd {1,3,5}, the coin is tossed twice.

S2 = {1HH, 1HT, 1TH, 1TT, 3HH, 3HT, 3TH, 3TT, 5HH, 5HT, 5TH, 5TT}

The required sample space is:

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

Answer:

Possible outcomes when a coin is tossed = {H,T}

Possible outcomes when a die is thrown = {1,2,3,4,5,6}

Let R1 and R2 denote the event that a red ball is drawn

and B1, B2, B3 denote the event that a blue ball is drawn

If H occurs, a die is thrown.

S1 = {H1, H2, H3, H4, H5, H6}

If T occurs, a ball from a box which contains $2$ red and $3$ black balls is drawn.

S2 = {TR1 , TR2 , TB1 , TB2 , TB3}

The required sample space is:

S = {TR1 , TR2 , TB1 , TB2 , TB3 , H1, H2, H3, H4, H5, H6}

Answer:

Given, a die is thrown repeatedly untill a six comes up.

Possible outcomes when a die is thrown = {1,2,3,4,5,6}

In the experiment 6 may come up on the first throw, or the 2nd throw, or the 3rd throw and so on till 6 is obtained.

The required sample space is:

S = {6, (1,6), (2,6), (3,6), (4,6), (5,6), (1,1,6), (1,2,6), ..., (1,5,6), (2,1,6). (2,2,6), ..., (2,5,6), ..., (5,1,6), (5,2,6), ... }

More About NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1:-

The first exercise of chapter 16 probability consists of questions related to outcomes of a random experiment and sample space of a random experiment. There are 16 questions in the Class 11 Maths chapter 16 exercise 16.1 solutions which you can solve by yourself. These questions are very basic based on the definition of sample space but will be useful in the upcoming exercises of this chapter. Before solving NCERT syllabus Class 11 Maths chapter 16 exercise 16.1 problems, you can go through the solved examples given in the NCERT book.

Also Read| Probability Class 11 Notes

Benefits of NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1:-

• NCERT solutions for Class 11 Maths chapter 16 exercise 16.1 are helpful for the students to learn about the random experiment and its outcomes, sample space.
• The classical theory of probability and the statistical approach of probability are two concepts that you have learned in this class.
• The axiomatic approach of probability required the basics of random experiment and sample space which you will learn in the Class 11 Maths chapter 16 exercise 16.1 solutions.

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Frequently Asked Questions (FAQs)

1. What is definition of random experiment ?

The random experiment is an observation that can be infinitely repeated under the same condition. The outcomes of random experiments are independent and identically distributed.

2. What is definition of outcome ?

The outcome is defined as the possible result of a random experiment

3. What is definition of sample space ?

The set of all possible outcomes of a random experiment is called sample space.

4. If we roll a die then what is the possible outcomes of this experiment ?

The outcomes of rolling a die are 1, 2, 3, 4, 5, or 6.

5. If we roll a die then what is the sample space this experiment ?

The sample space of rolling a die is  {1, 2, 3, 4, 5, 6}.

6. If two coins are tossed once then what the sample space of this experiment ?

Sample space of tossing two coins = { HH, HT, TH, TT} where H represents the head on the coin and T represents the getting tail on the coin.

7. A coin is tossed repeatedly until a head comes up what id the sample space of this experiment ?

Sample space of this experiment ( S) = {H, TH, TTH, TTTH, TTTTH,...}

8. What is the sample space when a coin is tossed and a die is thrown ?

Sample space of this experiment = { H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6 }

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