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RD Sharma is viewed as the best material for CBSE students. They are utilized all around the nation and are very useful for exam planning. The Class 12 RD Sharma chapter 30 exercise 30.4 solution is one of the examples for it. They are liked over NCERT because of their prospectus inclusion and detail of replies. The RD Sharma class 12th exercise 30.4 Probability can be utilized for self-practice and assessment of imprints.

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Probability Exercise 30.4 Question 1(i)

A= the first throw results in head, B= the last throw results in tail

Let,

Thus, A and B are independent events.

Probaility Exercise 30.4 Question 1(ii)

**Answer**: A and B are not independent events**Given: **A coin is tossed thrice and all the eight outcomes are assumed equally likely.

A= the number of heads is odd, B= the number of tails is odd**Hint: **Check, or not**Solution**: : As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Let,

Here

Thus, A and B are not independent events.

Probability Exercise 30.4 Question 1(iii)

Now,

A and B are not independent events.

Probability Exercise 30.4 Question 2

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Here, Total number of events = 36

A = The event of 4 on first die

B = Event of 5 on second die

Hence,A and B are independent events

Probability Exercise 30.4 Question 3(i)

A= the card is a king or queen, B= the card drawn is a queen or jack.

Let A = Event of King or Queen

….{No. of king and Queen are 4+4=8 and total outcomes=52}

B = Event of Queen or Jack

……{ No. of Jack and Queen are 4+4=8 and total outcomes=52}

…{No. of queen in a pack of cards =4}

Thus, A and B are not independent events.

Probability Exercise 30.4 Question 3(ii)

A= the card is black, B= the card drawn is a king

Let, A =Event of getting a black card

B = Event of getting an king

Thus, A and B are independent events.

Probaility Exercise 30.4 Question 3(iii)

A= the card is a spade, B= the card drawn is an ace

A = No. of cards is spade

B = No. of cards is ace

Thus, A and B are independent events.

Probability Exercise 30.4 Question 4(i)

A and B are independent events

Probaility Exercise 30.4 Question 4(ii)

Let,

Thus, B and C are not independent events.

Probability Exercise 30.4 Question 4(iii)

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

A and C are independent events

Probaility Exercise 30.4 Question 5

**Solution: **

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Thus, A and B are independent events.

Probability Exercise 30.4 Question 6(i)

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Probability Exercise 30.4 Question 6(iii)

Here A and B are independent events

Probaility Exercise 30.4 Question 6(v)

Answer:Hint: Using,

Given,

Solution:

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Probaility Exercise 30.4 Question 6(vi)

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Probability Exercise 30.4 Question 6(vii)

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Probability Exercise 30.4 Question 7

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Now,

Probability Exercise 30.4 Question 8

& are independent events

Let,

............(1)

Also

........(2)

Subtracting (1) from (2)

Substitute value of x in (2)

Solve using quadratic formula

Similarly

Probability Exercise 30.4 Question 9

**Hint**: Form events as a equation to solve

**Given,** A and B are independent events

**Solution:**

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Now,

...................(1)

Now, for

Where,

Probability Exercise 30.4 Question 10

Answer:Hint: Use

Given,

Solution:

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Let,

Probability Exercise 30.4 Question 11

Let, S= Total no. of dice in two throws

E=Getting a number greater than 3 on each toss

Probability Exercise 30.4 Question 12

B can solve the problem=

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

A can solve the problem =

i.e.,

B can solve the problem=

i.e.,

Similarly,

Probability Exercise 30.4 Question 13

Answer:Hint: Use

Given:

A = No. 4, 5 or 6 on first toss

B = 1, 2, 3 or 4 on second toss

Solution:

Probability Exercise 30.4 Question 14

Let 3 red balls be & and 2 black balls be & .

Total Possibilities =

i. Probability of drawing two red balls

ii. Probability of drawing two black balls

iii. Probability of first red and second black

Probability Exercise 30.4 Question 15

Three cards are drawn with replacement from a well shuffled pack of cards. Find the probability that the cards drawn are king, queen and jack.

Let,

A= Event of getting kings

Similarly, B= Event of getting queens

C= Event of getting jacks

Probability that cards drawn are king, queen and jack

(Permutations has been used because the order of king,queen and jack can be changed)

Probability Exercise 30.4 Question 16

Answer:Given: An article manufactured by a company consists of two parts X and Y. In the process of manufacture of the part X, 9 out of 100 parts may be defective. Similarly, 5 out of 100 are likely to be defective in the manufacture of part Y.

Hint:

Solution:

Let, A= Particle X is defective

B= Particle Y is defective

Required Probability

Probability Exercise 30.4 Question 17

Answer:Hint: Use,

Given, Possibilities

(A hits target)

(B hits target)

Solution: As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

(target will be hit by either A or B)

Probability Exercise 30.4 Question 18

Let,

P (Gun hits the plane) = 1 – (Gun does not hit the plane)

Probability Exercise 30.4 Question 19

**Answer**: i. ii. **Hint:** **Given:** The odds against event A are 5 to 2. The odds in flavor of event B are 6 to 5.**Solution**: As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

The odds against event A are 5 to 2.

The odds in flavor of event B are 6 to 5

- Probability of atleast one of the event occurs

ii P(none of the event occurred)

Probability Exercise 30.4 Question 20

P (Getting an odd number in one throw) …{there are 3 odd numbers in an throw of a dice}

Here, getting an odd number in three throws refers to 3 independent events

Probability Exercise 30.4 Question 21

Probability Exercise 30.4 Question 22(i)

Probability Exercise 30.4 Question 22(ii)

Probability Exercise 30.4 Question 22(iii)

Probability Exercise 30.4 Question 23

&

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Probability Exercise 30.4 Question 24

i.e,n(f)=10

i.e,n

Now,

Also,

So, no pair is independent.

Probability Exercise 30.4 Question 25(i)

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

As,

And A and B are independent events

i.e

Hence,

Probability Exercise 30.4 Question 25(ii)

And A and B are independent events

Hence,(A does not occur ,but B Occurs)

Probability Exercise 30.4 Question 25(iii)

As we know, Two events are said to be independent if the product of the events are equal to their intersection. i.e.

Given, A and B are independent events

As,

And A and B are independent vectors

So,

Hence,

Probability Exercise 30.4 Question 25(iv)

Given,

And A and B are independent events

i.e

Hence,

Probability Exercise 30.4 Question 26

Given,

Now, Let be the three days for which the signal is green and be the three days for not finding a green signal.

We have to find probability of finding green signal on consecutive two days out of three

So the event would be or

So the probability of finding green signal on consecutive two days out of three

The RD Sharma class 12 solution of Probability exercise 30.4, is utilized by thousands of students and educators for commonsense math information. The RD Sharma class 12th exercise 30.4 has 43 inquiries like Autonomous Occasions, Similarly possible Occasions, Comprehensive occasions, Association and crossing point, with substitution and without substitution based inquiries.

**The benefits of practicing from the RD Sharma class 12th exercise 30.4 are referred to beneath: -**

You can use RD Sharma class 12th exercise 30.4 material will assist students with improving comprehension of the chapter and score gold imprints in exams.

Career360 RD Sharma class 12 chapter 30 exercise 30.4 trusted in the scrutinizing material that different understudies have used. Teachers in like manner are particularly attached to the book concerning the subject of maths.

RD Sharma class 12th exercise 30.4 is given via Career360 free of cost for students to concentrate on problem-free.

RD Sharma class 12th exercise 30.4 solutions made by specialists and are refreshed to the most recent form of the book, which implies there would be no missing inquiries or additional inquiries.

- 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

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Download E-book1. What is the best mathematics reference material available online for class 12 students?

The presence of Class 12 RD Sharma Chapter 30 Exercise 30.4 is a gift to the current batch students. They must utilize it in the right way to score good marks.

2. Where can I find all the answers for the questions given in the 4th exercise of chapter 30?

The RD Sharma Class 12 Chapter 30 Solution provides the solved sums for all the 43 questions in it.

3. Are there any updates made in the RD Sharma solution books?

Frequent updates take place according to the changes made in the mathematics textbook.

4. In which website is the latest collection of RD Sharma reference books available?

The students can find the recent collection of the RD Sharma reference materials at the Career360 website.

5. Should only the class 12 students use the RD Sharma solution books?

The RD Sharma solution books can be used by class 11, 12 students and even teachers, tutors who handle classes for them.

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