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RD Sharma class 12th exercise 30.7 is undoubtedly one of the best NCERT solutions, which has been pretty much decided by high school students. These solutions are not your regular run-of-the-mill books that don't have a lot of information. The book is rich with new and modern calculations which are known to only a few experts. RD Sharma solutions These answers will hugely benefit high school students who struggle to find good study material for exam preparations. RD Sharma class 12 chapter 30 exercise 30.7 will end this tiring search and won't even require them to invest in any redundant study materials.

Probability exercise 30.7 question 2

Use baye’s theorem.

A bag A contained 2 white and 3 red ball and a bag B contain 5 red and 4 white ball one ball drawn at random from one of bag is found red. What is probability that it was drawn from bag B?.

The event selecting red ball denoted by R.

The event selected by bag A denoted by A.

The event selected by bag B denoted by B.

Bag A = 2 white and 3red ball.

Bag B = 4 white and 5 red ball.

Using Baye’s theorem

Probability exercise 30.7 question 3

Use baye’s theorem.

Three win contain 2 white and 3 black balls; 3 white, 2 black and 4 white and 1 black balls. One ball drawn from a win chosen at random and it was found to white. Find the probability of win drawn.

Let E

Let A be event that ball drawn white.

Using Baye’s theorem we get

Required probability

Probability exercise 30.7 question 5

Use baye’s theorem.

Suppose a girl throw a die. If she gets 1, 2 she toss a coin three times and note the number of tails. If she get 3, 4, 5, 6 she toss a coin once and note whether a head or tail is obtained. If she obtained exactly one tail, what is probability she threw 3, 4, 5, 6 with die.

Let E

Thus

Let E

{ (THH), (HTH), (HHT) }=3

If she tossed the coin once and exactly 1 tail show up then total favorable.

The probability that she threw 3, 4, 5, 6 with given that she got exactly one tail or in other word

Using Baye’s theorem we get

Probability exercise 30.7 question 6

Use baye’s theorem.

Let E = first group

F = second group

G = new product

We need to find probability that new product introduce was by second group.

i.e,

So,

P(E) = probability of first group win = 0.6

P(F) = probability of second group win = 0.4

Putting values in Baye’s theorem we get

Probability exercise 30.7 question 7

Use Baye’s theorem.

Suppose 5 men out of 100 and 25 women out of 1000 are good orator. An orator chose at random. Find the probability that make person is selected. Assume equal number of men and women.

Let A, E

Thus

Using Baye’s theorem we get

Probability exercise 30.7 question 8 maths

Use Baye’s theorem.

A letter is known to have come either from LONDON or CLIFTON on the envelope just two consecutive letter on are visible what is probability that letter has come from (i) LONDON (ii) CLIFTON

Let E

Thus

Let A be event come 2 consecutive letter on envelope are ON.

Then

And

Now

Using Baye’s theorem we get

i. Now

Using Baye’s theorem we get

Probability exercise 30.7 question 9

Use Baye’s theorem.

** **In class 5% of boy and 10% of girl have 10 of more than 150. In this class 60% of students boys.

If a student is selected at random and found to have 10 of more than 150. Find probability of student is boy.**Solution:**

Let E_{1} is the student chose boy and E_{2} is the student chose is girl.

Thus

Event E_{1} and E_{2} are mutually exclusive event A. a student have 10 more than 150.

Using Baye’s theorem we get

Multiplying every term by 10000

Probability exercise 30.7 question 10

0.1

Use Baye’s theorem.

A factor has three machines X, Y, Z producing 1000, 2000, 3000, bolts per day respectively. The machine X produce 1% defective bolts, Y produce 1.5% defective and Z produce 2% defective bolt.

Let E

Let A be event that bolt is defective.

Total bolt = 1000 + 2000 + 3000 = 6000

Using Baye’s theorem we get

Probability exercise 30.7 question 11

Use baye’s theorem.

An insurance company is used 3000, 4000, 5000 trucks. The probability of accident involving a scooter, a car, a truck 0.02, 0.03, 0.04, one insured vehicle meets with accident. Find the probability of (i) Scooter, (ii) car, (iii)Truck

Let E

Let A be event that vehicle meet an accident.

It is given that 3000 scooter, 4000 car and 5000 truck.

Total vehicle = 3000 + 4000 + 5000 = 12000

Using Baye’s theorem we get

Required probability

Required probability

Required probability

Probability exercise 30.7 question 12 maths

Use baye’s theorem.

Suppose we have four boxes A, B, C, D.

Box | Red | White | Black |

A | 1 | 6 | 3 |

B | 6 | 2 | 2 |

C | 8 | 1 | 1 |

D | 0 | 6 | 4 |

Let

R → event that red marble

A → event select box A

B → event select box B

C → event select box C

D → event select box D

Using Baye’s theorem

Using Baye’s theorem

Using Baye’s theorem

Probability exercise 30.7 question 13

Use Baye’s theorem.

The first operator A produce 10% defective items whereas the two other operate B, C 5% and 7% defective respectively. A is an on 50% of time, B on job 30% of time and C on job 20% of time. The defective item is produced by A.

Let E

Let X be event produce defective item

The probability that defective item was produce by A is given as

Using Baye’s theorem we get

Probability exercise 30.7 question 14

Use Baye’s theorem.

50% of manufacture on machine A, 30% on B and 20% on C. 2% of item produced on A and 2% item produce on B are defective and 3% of these produce on C.

Let

E

E

E

Let E be event that item defective.

Using Baye’s theorem we get

Probability exercise 30.7 question 15

Use Baye’s theorem.

There are three coins. One is two headed coin another is biased coin that come up head 75% of time and third is also a biased coin that come up tall 40% of time. One of three coins is chosen at random and tossed and it show head. What is the probability that it was two head coins.

E

E

E

A be the event that head comes.

Then,

Using Baye’s theorem we get

Probability exercise 30.7 question 16 maths

0, 2

Use Baye’s theorem.

In factory machine produce 30% total item B produce 25% and C produce remaining output. If defective item produce by machine A, B, C is 1%. 12% and 2% respectively. Three machines working together produce 10,000 item in day. An item is drawn at random from day output and found defective. Find probability that was produce by machine A.

Let E

E

E

E

A=total event that item is defective

Using Baye’s theorem we get

Probability exercise 30.7 question 18

Use Baye’s theorem.

Three win A, B, C contain 6 red and 4 white; 2 red, 6 white and 1 red 5 white ball respectively. A win is chosen at random and ball is drawn. If ball drawn is found to red. Find the probability that ball from win A.

Let E

Using Baye’s theorem we get

Probability exercise 30.7 question 19

Use Baye’s theorem.

In group of 400 people 160 smoke and non-vegetarians, 100 smoke and vegetarians. The probability of getting chest disease 35%, 20%, 10% respectively. A person chosen from group at found suffering. Find probability selected person smoke non vegetarian.

Let us denote group of smoker and non-vegetarian as A.

B = smoker and non-vegetarian

C = no smoker and vegetarian

No of people in group A = 160;

No of people in group B = 100;

No of people in group C = 400 - 260 = 140;

Probability of disease person from group A is

Using Baye’s theorem we get

Probability exercise 30.7 question 20 maths

Use Baye’s theorem.

Let E

D = defective item

Total production = 100 + 200 + 300 = 600

Using Baye’s theorem we get

Probability exercise 30.7 question 21

Use Baye’s theorem.

A bag contain 1 white and 6 red ball, and second bag contain 4 white 3 red. One of the bags is pick at random and ball is randomly drawn from college to white in color.

Let E

E

A=The white ball drawn random

Using Baye’s theorem we get

Probability exercise 30.7 question 22

Use Baye’s theorem.

In certain college 4% of boy and 1% of girl are taller than 1.75 meter. Furthermore 60% of student in colleges are girl. A student selected at garden from college is found be taller 1.75 meter.

Let E

A denoted the student is 1.75m tall.

Using Baye’s theorem we get

Probability exercise 30.7 question 24 maths

Use Baye’s theorem.

The person A, B, C applies for job of manager in private company. Chance of their selection is in ratio 1:2:4. The probability that A, B, C can introduce change to improve profit of company are 0.8, 0.5, 0.3 respectively.

Let E

Using Baye’s theorem we get

Probability exercise 30.7 question 25

Use Baye’s theorem.

An insurance company insures 2000 scooter and 3000 motorcycle. The probability of an accident involve scooter is 0.01 and that of motorcycle.

Using Baye’s theorem we get

Probability exercise 30.7 question 26

Use Baye’s theorem.

It is known that 60%beside in a hostel and 40% don’t reside in hostel. Previous year results report that 30% of student residing in hostel attain. A grade and 20% of ones not residing in hostel attain.

Let A denotes A -grade

H denote from hostel

D denote day scholar

Using Baye’s theorem we get

Probability exercise 30.7 question 27

Use Baye’s theorem.

There are three coins one is two headed coin, another is blazed coin that comes up heads 75% of time and third is unbiased coin.

Let

C

C

C

We need to find probability that coin is two headed it show

Using Baye’s theorem we get

Probability exercise 30.7 question 28 maths

Use Baye’s theorem.

Assume that chance of patient having a heart attack is 40%. If is also assumed that meditation and yoga source reduce the rest of heart attack by 30% and preparation of certain drug reduce its chance by 25%.

Let A

Using Baye’s theorem we get

Probability exercise 30.7 question 29

Use baye’s theorem.

Box | Colour | |||

Black | White | Red | Blue | |

I | 3 | 4 | 5 | 6 |

II | 2 | 2 | 2 | 2 |

III | 1 | 2 | 3 | 1 |

IV | 4 | 3 | 1 | 5 |

Let A: Event that is black ball is selected

E

E

E

E

Using Baye’s theorem we get

Probability exercise 30.7 question 30

Use Baye’s theorem.

If machine is correctly set up it produce 90% acceptable item. If it incorrectly set up the produce 40% acceptable item. Past experience show 80% of setup is correctly done. If after certain set up the machine produce 2 acceptance items.

Let A be event that machine produce 2 acceptable item.

E

E

Using Baye’s theorem we get

Probability exercise 30.7 question 31

Use Baye’s theorem.

Bag A contain 3 red, 5 black, white bag contain 4 red and 4 black. Two ball are transferred at random from bag A to bag B and then a ball B drawn from bag B at random..

2 ball drawn from bag A could be both red probability =

2 one red and one black probability =

3 both black probability =

The no of ball in bag B in each case would be

1. 6 red 4 black = probability pick red =

2. 5 red 5 black = probability pick red =

3. 4 red 6 black = probability pick red =

Probability of two red ball transfer under the condition that red ball found

Using Baye’s theorem we get

Probability exercise 30.7 question 32 maths

Use Baye’s theorem.

Probability that T.B is detected when a person is actually suffering is 0.99. The probability that doctor diagnose incorrectly that person has T.B on basis of x-ray is 0.001. In certain city 1 in 1000 person suffer from T.B.

Let

E

E

E=Event that person is diagnose to have T.B

And

Using Baye’s theorem we get

Probability exercise 30.7 question 33

The test will correctly detect the disease 1% of time probability large population of which an estimate 0.2% has disease a person.

Let A,E

Now

Using Baye’s theorem we get

Probability exercise 30.7 question 34

D

1800 had disease d

Let A, E

Now,

Using Baye’s theorem we get

Required probability

Required probability

Required probability

As

is maximum, so, it is most likely that the person suffer from the disease d_{1}.

Probability exercise 30.7 question 35

A is known to speak with 3 time out of 5 time. He throws a die and report that is one. Find the probability that actually one.

Let A, E

Now,

Using Baye’s theorem we get

Required probability

Probability exercise 30.7 question 36 maths

A speaks the truth 8 time out of 10 time a die is tossed. He report that it was 5.

Let A denote the event that man reports 5 occur and E the event that actually 5 tossed up.

Also,

=Probability that man reports that 5 occur given that 5 actually turned up

= probability of man speak the truth

Probability that man reports that 5 occur given that 5 does not turned up

= probability of man not speak the truth

Using Baye’s theorem we get

Required probability

Probability exercise 30.7 question 37

Use baye’s theorem.

In answering a question on multiple choice tests, students either answers or guess. Assume the student who guess at answer will correct with probability

Let

A = student know answer

B= student guess

C = student answer correctly

We know to find probability that student know answer if he answer is correctly.

Using Baye’s theorem we get

Required probability

Probability exercise 30.7 question 38

Use Baye’s theorem.

A lab blood test 99% effective in detecting certain when its infection is present. However, the test yield a false positive result for 0.5% of healthy person 0.01% of population actually has disease.

Let E

Since, E

Let A be event that blood test positive.

Probability that a person have disease given that his result positive

Using Baye’s theorem we get

Probability exercise 30.7 question 39

Use Baye’s theorem.

There are three categories of student in class 60 student.

A very hardworking, B = regular but not hardworking, C = careless and irregular, 10 student are category A, 30 in B, rest in C. if found that probability of student of category A unable to get good marks in final year, probability of student in exam is 0.002 of category B is 0.02 and category C is 0.20.

Let

E

E

E

S=Student not get good marks

Using Baye’s theorem we get

Required probability

Probability exercise 30.7 question 1

33/118, 55/118, 30/118

Use baye’s theorem.

The content of win I, II, III is as follows

Win I; 1 white, 2 black and 3 red balls.

Win II: 1 black, 2 white and 1 red balls,

Win III: 4 white, 5 black, 3 red balls

One win is chosen at random and two balls are drawn. The happen to be white and red what is probabilities that come from win I, II, III.

Let E

Let A be event of chosen two ball (w,R).

Using Bayes’ theorem we get

Required probability

Required probability

Required probability

Probability exercise 30.7 question 4 maths

Use baye’s theorem.

The content of three win

Win I: 7 white, 3 black;

Win II: 4 white, 6 black

Win III: 2 white 8 black

One ball drawn as random with probability 0.20, 0.60, 0.20 respectively drawn chosen win two balls drawn random without replacement. If both these ball drawn what is probability came from win III?

Let E

Let A be event of two balls drawn white.

Using Baye’s theorem we get

Probability exercise 30.7 question 17

Use Bayes theorem.

The first plant manufacture 60% of bicycle and second plant 40% out of that 80% of bicycle are rated of standard quality at first plant and 90% of standard quality at second plant.

E

E

A be event the cycle is standard

Using Baye’s theorem we get

Probability exercise 30.7 question 23

Use Baye’s theorem.

From A, B, C chance of being selected as manager of firm in ratio 4:1:2 respectively. The respectively probability for them a radical change in marketing strategy, 0.3, 0.8, 0.5.

Let E

Using Baye’s theorem we get

Among the various maths Solutions of RD Sharma, the RD Sharma class 12 solutions Probability 30.7 deserves a special mention for its quality of answers. Exercise 30.7 has 39 questions which are based on Baye’s theorem and Conditional probability. The class 12th exercise 30.7 will guide you on how to solve these problems and find accurate answers.

The class 12 RD Sharma chapter 30 exercise 30.7 solution should definitely be availed by all students of mathematics in class 12. The RD Sharma class 12 solutions chapter 30 ex 30.7 comes with a ton of benefits which are listed below:-

RD Sharma class 12 chapter 30 exercise 30.7 provides answers to all NCERT questions no matter which edition of the textbook you use. The pdf is updated regularly so that students may find all the answers they will require for exams.

The RD Sharma class 12 solutions Probability 30.7 contains some new and improved techniques and calculations that can be used by students to solve questions. Experts have created these answers so students can be sure they are accurate and trustworthy.

RD Sharma class 12 chapter 30 exercise 30.7 will be an excellent book to solve homework questions because teachers use these answers to check students' progress in class. If students practice this book well, they will even find common questions in boards.

The answers in RD Sharma class 12 chapter 30 exercise 30.7 can be used by students to test themselves at home. They will be able to solve questions on their own and compare answers to test their performance and keep up with regular lessons.

It is pretty difficult to find good study materials for exams without breaking the bank. The RD Sharma class 12 chapter 30 exercise 30.7 comes free of cost and the pdf can be downloaded from Career360.

- 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 are the concepts covered under RD Sharma class 12 solutions Probability 30.7?

The concepts that are covered in chapter 30 of the RD Sharma class 12 solutions Probability 30.7 are conditional probability, multiplication rule, random variables, Bayes theorem, Bernoulli Trials, Binomial Distribution.

2. How many questions are there in RD Sharma class 12 solutions Probability 30.7?

There are a total of 39 questions in the RD Sharma class 12 solutions Probability 30.7 book

3. What are the advantages of referring to the RD Sharma Class 12th Exercise 30.7 solution guide for exam preparation?

The RD Sharma Class 12th Exercise 30.7 is comparatively better than the reference materials for the class 12 students. Here are some of its advantages listed:

The solutions are framed by experts in respective domains.

Sums solved in numerous methods.

Available for free at the Career 360 website.

4. Which is the best NCERT solution?

The RD Sharma solutions are hands-down the best NCERT solutions that students will find in the market. Numerous students and teachers in India have recommended this book for exam preparations.

5. How can I download the RD Sharma class 12th exercise 30.7 pdf?

Students will be able to download the RD Sharma class 12th exercise 30.7 from

Mar 22, 2023

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