# SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 3 - Binomial Distribution [Latest edition]

## Chapter 3: Binomial Distribution

MCQ

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 3 Binomial Distribution MCQ

#### 2 Marks

MCQ | Q 1

In a Binomial distribution with n = 4, if 2P(X = 3) = 3P(X = 2), then value of p is ______

• 9/13

• 4/13

• 6/13

• 7/13

MCQ | Q 2

Given that X ~ B(n, p). If n = 10, p = 0.4, then E(X) = ______

• 1

• 2

• 3

• 4

MCQ | Q 3

For X ~ B(n, p), if V(X) = 2.4 and p = 0.4, then n = ______

• 10

• 20

• 30

• 40

MCQ | Q 4

Given that X ~ B(n = 10, p), E(X) = 8, then value of p = ______

• 0.4

• 0.8

• 0.6

• 0.7

MCQ | Q 5

Bernoulli distribution is a particular case of binomial distribution if n = ______

• 4

• 10

• 2

• 1

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 3 Binomial Distribution Very Short Answers

#### 1 Mark

Very Short Answers | Q 1

If X ~ B(n, p), E(X) = 12, V(X) = 4, then find n

Very Short Answers | Q 2

For Bernoulli Distribution, state formula for E(X) and V(X).

Very Short Answers | Q 3

For X ~ B(n, p) and P(X = x) = ""^8"C"_x(1/2)^x (1/2)^(8 - x), then state value of n and p

Very Short Answers | Q 4

State the formula for p.m.f. of Binomial Distribution

Very Short Answers | Q 5

A die is thrown. If X denotes the number of positive divisors of the outcomes, then find the range of random variable X

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 3 Binomial Distribution Short Answers I

#### 2 Marks

Short Answers I | Q 1

A r.v. X ~ B(n, p). If the values of mean and variance of X are 18 and 12 respectively, then find total number of positive values of X.

Short Answers I | Q 2

Given X ~ B(n, p). If E(X) = 6, V(X) = 4.2, find n and p

Short Answers I | Q 3

If X ~ B(n, p) with n = 10, p = 0.4, then find E(X2).

Short Answers I | Q 4

If X ~ B(6, p) and 2P(X = 3) = P(X = 2), then find p

Short Answers I | Q 5

Let the p.m.f. of r.v. X be P(x) = ""^4"C"_x (5/9)^x (4/9)^(4 - x), x = 0, 1, 2, 3, 4. Find E(X) and Var(X)

### SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 Chapter 3 Binomial Distribution Short Answers II

#### 3 Marks

Short Answers II | Q 1. a)

A Fair coin is tossed 5 times, find the probability that coin shows exactly three times head

Short Answers II | Q 1. b)

A fair coin is tossed 5 times, find the probability that no head

Short Answers II | Q 2

The probability that certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive

Short Answers II | Q 3

Find the probability of guessing correctly at least nine out of ten answers in a "true" or "false" objective test

Short Answers II | Q 4. i)

A fair coin is tossed 8 times. Find the probability that it shows heads exactly 5 times

Short Answers II | Q 4. ii)

A fair coin is tossed 8 times. Find the probability that it shows heads at least once

Short Answers II | Q 5. a)

The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation none will recover

Short Answers II | Q 5. b)

The probability that a person who undergoes a kidney operation will be recovered is 0.5. Find the probability that out of 6 patients who undergo similar operation half of them recover.

## SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 3 - Binomial Distribution

SCERT Maharashtra Question Bank solutions for 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 3 (Binomial Distribution) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in 12th Standard HSC Mathematics and Statistics (Arts and Science) Maharashtra State Board 2022 chapter 3 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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