# Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 8 - Binomial Distribution [Latest edition]

## Chapter 8: Binomial Distribution

Exercise 8.1Miscellaneous exercise 8
Exercise 8.1 [Pages 251 - 252]

### Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 8 Binomial Distribution Exercise 8.1 [Pages 251 - 252]

Exercise 8.1 | Q 1.1 | Page 251

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of 5 successes.

Exercise 8.1 | Q 1.2 | Page 251

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at least 5 successes.

Exercise 8.1 | Q 1.3 | Page 251

A die is thrown 6 times. If ‘getting an odd number’ is a success, find the probability of at most 5 successes.

Exercise 8.1 | Q 2 | Page 251

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.

Exercise 8.1 | Q 3 | Page 251

There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?

Exercise 8.1 | Q 4.1 | Page 251

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that all the five cards are spades.

Exercise 8.1 | Q 4.2 | Page 251

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that only 3 cards are spades

Exercise 8.1 | Q 4.3 | Page 251

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that none is a spade.

Exercise 8.1 | Q 5 | Page 251

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs

(i) none

(ii) not more than one

(iii) more than one

(iv) at least one

will fuse after 150 days of use.

Exercise 8.1 | Q 6 | Page 252

A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?

Exercise 8.1 | Q 7 | Page 252

On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?

Exercise 8.1 | Q 8.1 | Page 252

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100} .$  What is the probability that he will win a prize at least once.

Exercise 8.1 | Q 8.2 | Page 252

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100} .$  What is the probability that he will win a prize exactly once.

Exercise 8.1 | Q 8.3 | Page 252

A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is $\frac{1}{100} .$  What is the probability that he will win a prize at least twice.

Exercise 8.1 | Q 9.1 | Page 252

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that none of the floppy disc work.

Exercise 8.1 | Q 9.2 | Page 252

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly one floppy disc work.

Exercise 8.1 | Q 9.3 | Page 252

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly two floppy disc work.

Exercise 8.1 | Q 9.4 | Page 252

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that all 3 of the sample will work.

Exercise 8.1 | Q 10 | Page 252

Find the probability of throwing at most 2 sixes in 6 throws of a single die.

Exercise 8.1 | Q 11 | Page 252

It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles, 9 are defective?

Exercise 8.1 | Q 12.1 | Page 252

Given X ~ B(n, P) if n = 10 and p = 0.4, find E(x) and Var(X).

Exercise 8.1 | Q 12.2 | Page 252

Given X ~ B(n, P) if p = 0.6 and E(X) = 6, find n and Var(X).

Exercise 8.1 | Q 12.3 | Page 252

Given X ~ B(n, P) if n = 25 and E(X) = 10, find p and SD(X).

Exercise 8.1 | Q 12.4 | Page 252

Given X ~ B(n, P) if n = 10, E(X) = 8, find Var(X).

Miscellaneous exercise 8 [Page 253]

### Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 8 Binomial Distribution Miscellaneous exercise 8 [Page 253]

Miscellaneous exercise 8 | Q 1 | Page 253

Choose the correct option from the given alternatives:

A die is thrown 100 times. If getting an even number is considered a success, then the standard deviation of the number of successes is

• sqrt50

• 5

• 25

• 10

Miscellaneous exercise 8 | Q 2 | Page 253

Choose the correct option from the given alternatives:

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

• 128/256

• 219/256

• 37/256

• 28/256

Miscellaneous exercise 8 | Q 3 | Page 253

Choose the correct option from the given alternatives:

For a binomial distribution, n = 5. If P(X = 4) = P(X = 3), then p = ______

• 1/3

• 3/4

• 1

• 2/3

Miscellaneous exercise 8 | Q 4 | Page 253

Choose the correct option from the given alternatives:

For a binomial distribution, n = 4. If 2P(X = 3) = 3P(X = 2), then p = ______

• 4/13

• 5/13

• 9/13

• 6/13

Miscellaneous exercise 8 | Q 5 | Page 253

Choose the correct option from the given alternatives:

If X ~ B(4, p) and P(X = 0) = 16/81, the P(X = 4) = ______

• 1/16

• $\frac{1}{81}$

• $\frac{1}{27}$

• $\frac{1}{8}$

Miscellaneous exercise 8 | Q 6 | Page 253

Choose the correct option from the given alternatives:

The probability of a shooter hitting a target is 3/4 How many minimum numbers of times must he fire so that the probability of hitting the target at least once is more than 0·99?

• 2

• 3

• 4

• 5

Miscellaneous exercise 8 | Q 7 | Page 253

Choose the correct option from the given alternatives:

If the mean and variance of a binomial distribution are 18 and 12 respectively, then n =

• 36

• 54

• 18

• 27

Miscellaneous exercise 8 [Pages 253 - 524]

### Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board Chapter 8 Binomial Distribution Miscellaneous exercise 8 [Pages 253 - 524]

Miscellaneous exercise 8 | Q 1.1 | Page 253

Let X ~ B(10, 0.2). Find P(X = 1).

Miscellaneous exercise 8 | Q 1.2 | Page 253

Let X ~ B(10, 0.2). Find P(X ≥ 1).

Miscellaneous exercise 8 | Q 1.3 | Page 253

Let X ~ B(10, 0.2). Find P(X ≤ 8).

Miscellaneous exercise 8 | Q 2.1 | Page 253

Let X ~ B(n, p) if n = 10, E(X) = 5, find p and Var(X).

Miscellaneous exercise 8 | Q 2.2 | Page 253

Let X ~ B(n, p) if E(X) = 5 and Var(X) = 2.5, find n and p.

Miscellaneous exercise 8 | Q 3.1 | Page 253

If a fair coin is tossed 10 times and the probability that it shows heads 5 times.

Miscellaneous exercise 8 | Q 3.2 | Page 253

If a fair coin is tossed 10 times and the probability that it shows heads in the first four tosses and tail in last six tosses.

Miscellaneous exercise 8 | Q 4 | Page 254

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 2 will miss the target.

Miscellaneous exercise 8 | Q 5.1 | Page 254

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: exactly one has a burst tyre

Miscellaneous exercise 8 | Q 5.2 | Page 254

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: at most three have a burst tyre

Miscellaneous exercise 8 | Q 5.3 | Page 254

The probability that a mountain-bike travelling along a certain track will have a tyre burst is 0.05. Find the probability that among 17 riders: two or more have burst tyre.

Miscellaneous exercise 8 | Q 6 | Page 254

The probability that a lamp in a classroom will be burnt out is 0.3. Six such lamps are fitted in the class-room. If it is known that the classroom is unusable if the number of lamps burning in it is less than four, find the probability that the classroom cannot be used on a random occasion.

Miscellaneous exercise 8 | Q 7 | Page 254

A lot of 100 items contain 10 defective items. Five items are selected at random from the lot and sent to the retail store. What is the probability that the store will receive at most one defective item?

Miscellaneous exercise 8 | Q 8 | Page 254

A large chain retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 3%. The inspector of the retailer picks 20 items from a shipment. What is the probability that the store will receive at most one defective item?

Miscellaneous exercise 8 | Q 9 | Page 524

The probability that a certain kind of component will survive a check test is 0.5. Find the probability that exactly two of the next four components tested will survive.

Miscellaneous exercise 8 | Q 10 | Page 254

An examination consists of 10 multiple choice questions, in each of which a candidate has to deduce which one of five suggested answers is correct. A completely unprepared student guesses each answer completely randomly. What is the probability that this student gets 8 or more questions correct? Draw the appropriate morals.

Miscellaneous exercise 8 | Q 11.1 | Page 254

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that all 8 machines.

Miscellaneous exercise 8 | Q 11.2 | Page 524

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that 7 or 8 machines.

Miscellaneous exercise 8 | Q 11.3 | Page 254

The probability that a machine will produce all bolts in a production run within specification is 0.998. A sample of 8 machines is taken at random. Calculate the probability that at most 6 machines will produce all bolts within specification.

Miscellaneous exercise 8 | Q 12 | Page 254

The probability that a machine develops a fault within the first 3 years of use is 0.003. If 40 machines are selected at random, calculate the probability that 38 or more will develop any faults within the first 3 years of use.

Miscellaneous exercise 8 | Q 13.1 | Page 254

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 0.

Miscellaneous exercise 8 | Q 13.2 | Page 254

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 1.

Miscellaneous exercise 8 | Q 13.3 | Page 254

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 2.

Miscellaneous exercise 8 | Q 13.4 | Page 254

A computer installation has 10 terminals. Independently, the probability that any one terminal will require attention during a week is 0.1. Find the probabilities that 3 or more, terminals will require attention during the next week.

Miscellaneous exercise 8 | Q 14.1 | Page 255

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Calculate the probabilities of obtaining an answer yes from 0, 1, 2, 3, 4 of the pupils.

Miscellaneous exercise 8 | Q 14.2 | Page 255

In a large school, 80% of the pupil like Mathematics. A visitor to the school asks each of 4 pupils, chosen at random, whether they like Mathematics.
Find the probability that the visitor obtains answer yes from at least 2 pupils:
a. when the number of pupils questioned remains at 4.
b. when the number of pupils questioned is increased to 8.

Miscellaneous exercise 8 | Q 15.1 | Page 255

It is observed that it rains on 12 days out of 30 days. Find the probability that it rains exactly 3 days of week.

Miscellaneous exercise 8 | Q 15.2 | Page 255

It is observed that it rains on 12 days out of 30 days. Find the probability that it it will rain at least 2 days of given week.

Miscellaneous exercise 8 | Q 16 | Page 255

If the probability of success in a single trial is 0.01. How many trials are required in order to have a probability greater than 0.5 of getting at least one success?

Miscellaneous exercise 8 | Q 17 | Page 255

In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.

## Chapter 8: Binomial Distribution

Exercise 8.1Miscellaneous exercise 8

## Balbharati solutions for Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 8 - Binomial Distribution

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Concepts covered in Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board chapter 8 Binomial Distribution are Bernoulli Trial, Binomial Distribution, Mean of Binomial Distribution (P.M.F.), Variance of Binomial Distribution (P.M.F.), Bernoulli Trials and Binomial Distribution.

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