# 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

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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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