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Every reputed CBSE institution recommends their students to use the RD Sharma Solution books to clarify their doubts at home. However, even though the teachers provide their best in making the students understand the concepts, they only encounter doubts when they learn the concept. And this takes place a lot many times while doing homework in maths. For example, the sums in the chapter Probability make the students perplexed if they are unclear about the concept. And here is where the RD Sharma Class 12th Chapter 30 VSA comes to the rescue.

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Probablity Exercise very short answer question, question 3

Hint:

Three digit number cannot start with 0 , and hundredth place can have any of the 4 digits.

Given:

Given digits are 0,2,4,6 and 8 . We have to form a number using digits 0,2,4, 6 and 8 .

Explanation:

Since a three digit number cannot begin with the digit 0. The hundredth place can have any of the 4 digits. Also tens & units place can have all the 5 digits.

So S = total possibilities for 3 -digit numbers

Let A be the event of three digit numbers having all digits same =4

nA=4

Thus,

Probablity Exercise very short answer question, question 4

Hint:

Given:

Three numbers are chosen at random from 1 to 20.

Explanation:

Let S be a sample space. A cube has 6 faces

Total Possible Outcomes in 5 throws =

So

Let A be any event of getting 7 is by getting two 2’s and one 3’s

Thus , The required probability is

lease solve RD sharma class 12 chapter 30 Probablity Exercise very short answer question, question 4 maths textbook solutio

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Probablity Exercise very short answer question, question 1

Hint:

Let 'S be set of all number formed by the digits 1,2,3,5 & 'A be the event of getting a number divisible by 5 .

So

Given:

Given digits a re 1,2,3 & 5

Explanation:

Assume S be set of all number formed by 1,2,3 and 5

A be the event of of getting a number divisible by 5.

n(s)= Number of numbers formed by

So

This, the probability that the number is divisible by 5 is .

Probablity Exercise very short answer question, question 2

Hint:

Given:

Three dice are thrown

Explanation:

It is given that ,

S = Three dice are thrown.

n(S)= total number of sample space

= 216

A be an event of getting 4 or 5 on each of the dice simultaneously

So, n(A)=8

At

Thus, required probability is

The probability of getting 4 or 5 on each of the dice simultaneously is

Probablity Exercise very short answer question, question 5

Hint:

The possible way of getting 7w by getting two 2’s and one 3’s

Given:

An ordinary cube has 4 plane faces, one face marked 2 and another face marked 3

Explanation:

Probability is given that,

Three numbers are chosen at random from 1 to 20

Total Number of cases = 18

So, the required probability =

Hence, the probability that they are consecutive is

Probablity Exercise very short answer question, question 6

Hint:

Assume six girls as one person

Given:

Six boys and 6 girls sit in a row at random.

Explanation:

Let S be the sample space of arrangement of six boys and six girls.

Let A be an event that all girl sit together.

Hence, the required probability is

Probablity Exercise very short answer question, question 7

Hint:

and

If A & B are independent then

Given

Explanation:

It is given that,

We know,

(since, A and B are Independent)

Also, we know,

Thus, P(B)=

Probablity Exercise very short answer question, question 8

Hint:

Given:

A die is rolled four times

Explanation:

When a die is rolled ,

S = Total No. of outcomes

= {1,2,3,4,5,6}

n(S) = 6

Let A be an event of getting not less than 2 & not greater than 5.

⇒ A={2,3,4,5}

n(A)=4

Since a die is rolled four times so, the probability in getting four throws

Thus, the required probability is =

Probablity Exercise very short answer question, question 9

Hint:

P(exactly one of 2 events occurs) =

Given:

A and B are two events

Explanation:

It is given that ,

A & B are two events

We need to find expression such that exactly one of two events occurs

P( Exactly one of 2 everts occurs )

Hence , The required expression is

Probablity Exercise very short answer question, question 10

Hint:

Identify number from the set of {1,2,………..100] which are perfect cube & hence find probability.

Given:

Given set of number is {1,2, 3,……….100}

Explanation:

S = {1,2,3………………….100}

n(S) = 100

Let A be the event that the number is cube.

A = {1,8,27,64}

n(A)=4

Hence the required probability is

probablity exercise Very short answer question, question 11

Hint:

Use the formula,

Given:

Explanation:

It is given that

Let A denoted the probability that A wins.

We know,

Now, the probability that A losses us

Thus, the required probability is

Probablity exercise Very short answer question, question 13

Hint:

Given:

and

Then

Explanation:

We have

and

According to bay’s theorem

Now

Where U=universal set

So

Therefore

Probablity exercise Very short answer question, question 14

Hint:

If A & B are independent then

Given:

A & B are two independent events

Explanation:

It is given that , A & B are independent

We know,

{ A & B are independent }

Hence,

Probablity exercise Very short answer question, question 15

Hint:

Using the formula,

first find

Then using the relation, ,

Find the required value

Given:

P(A) = 0.3

P(B) = 0.6

P(B|A) = 0.5

Explanation:

We know ,

We know ,

Hence ,

Probablity exercise Very short answer question, question 16

Hint:

Use the relation ,

P(atleast two of A,B,C occurs) =

Given:

A, B & C are three independent events such that

Explanation:

We have,

Now,

P(atleast two of A,B,C occurs) =

( A , B & C are independent )

Probablity exercise Very short answer question, question 17

Hint:

If A and B are independent then and

P(exactly one of the two events occurs) =

Given:

A and B are independent events

Explanation:

It is given that ,

A and B are independent events

Now ,

P(exactly one of the two events occurs) =

( A , B are independent)

Hence, the required expression is

Probablity exercise Very short answer question, question 18

Hint:

If A and B are independent then,

and

P(exactly one of the two events occurs) =

Given:

A and B are independent events such that

P(A) = p

P(B) = 2p

P(exactly one of A and B occurs) =

Explanation:

It is given that

P(exactly one of A and B occurs) =

[ since,PA ∩B=PAPB]

⇒

Using quadratic formula, we have

Hence, the value of p is or

Chapter 30, Probability, has seven exercises in total, ex 30.1 to ex 30.7. However, when it comes to the Very Short Answer (VSA) part, most students get confused on how to solve quickly. There are eighteen questions in the VSA section. The concepts included here are the probability of dice, divisibility, coins, cards, the occurrence of two events based on Union and intersection, with replacement and without replacement, binomial, random variable and mutually exclusive event. If the students struggle to guess the exact formula used in these concepts, they can refer to the RD Sharma Class 12 Solutions Chapter 30 VSA book.

One challenging task in solving the VSA part is that the solutions must be short and direct. Therefore, the usage of tricks and shortcuts is highly encouraged. RD Sharma Solutions If the students are unaware of it, they spend much time in this portion during exams. The RD Sharma Class 12th Chapter 30 VSA solution material provides the students with various shortcuts to solve the probability sums. As it follows the NCERT syllabus, the CBSE students feel it is easy to cross their benchmark scores.

The Class 12 RD Sharma Chapter 30 VSA Solution material solutions are provided and verified by experts in the respective domain. Various practice questions make the students used to the VSA type questions. This eventually makes them save time during the examination, which they can spend on rechecking the answers and correcting their mistakes.

The students can use the RD Sharma Class 12 Solutions Probability Chapter 30 VSA book while they encounter doubts in their homework assignments. The Career360 website gives access for everyone to view and download the RD Sharma Class 12th Chapter 30 VSA reference material for free of cost.

The questions for the public exams are also taken from the RD Sharma books. Therefore, the RD Sharma Class 12 Solutions Chapter 30 FBQ helps the students prepare for their public exams effortlessly. Various students have benefitted by using these books for their public exams. So, download your copy of RD Sharma books and commence the preparation for the public exams.

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Which solution book helps the student attain ideas on how to write the VSA part for chapter 30?

The RD Sharma Class 12th Chapter 30 VSA reference material gives the student an idea of how exactly the VSA part must be answered.

2. Is there any best solution for the students to refer to the VSA of the probability chapter?

The RD Sharma Class 12th Chapter 30 FBQ provides the best set of solutions given by the experts and makes the students score high marks in the exams.

3. On which website can the RD Sharma PDFs be available?

The RD Sharma books are available on the Career 360 website. Anyone can access and download these PDF materials.

4. How many VSA questions are present the class 12, mathematics chapter 30?

There are eighteen questions asked in class 12, mathematics chapter 30 textbook. The students can use the RD Sharma Class 12th Chapter 30 VSA to refer to the solutions.

5. How much does the RD Sharma reference material cost?

The authorized RD Sharma solution’s PDF can be downloaded from the Career 360 website for free.

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