NCERT Solutions For Class 12 Maths Chapter 13 Probability Ex 13.4

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NCERT Solutions for Class 12 Maths Chapter 13 Probability Ex 13.4

The topics and sub-topics included in Chapter 13 Probability the following:

Section Name Topic Name
13 Probability
13.1 Introduction
13.2 Conditional Probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes’ Theorem
13.6 Random Variables and its Probability Distributions
13.7 Bernoulli Trials and Binomial Distribution

NCERT Solutions for Class 12 Maths Chapter 13 Probability 13.4 are part of NCERT Solutions for Class 12 Maths. Here we have given Class 12 Maths NCERT Solutions Probability Ex 13.4

Class 12 Maths Probability Solutions

Question 1.
State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
NCERT Solutions for Class 12 Maths Chapter 13 Probability 1
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 1

Question 2.
An urn contains 5 red and 2 black balls. Two balls are randomly drawn. Let X represent the number of black balls. What are the possible values of X ?. Is X a random variable?
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 2

Question 3.
Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed 6 times. What are possible values of X?
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 3

Question 4.
Find the probability distribution of
(a) number of heads in two tosses of a coin.
(b) number of tails in the simultaneous tosses of three coins.
(c) number of heads in four tosses of a coin.
Solution:
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 4
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 4 - i
Class 12 Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 4 - ii

Question 5.
Find the probability distribution of the number of successes in two tosses of a die where a success Is defined as
(i) number greater than 4
(ii) six appears on at least one die
Solution:
Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 5

Question 6.
From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement Find the probability distribution of the number of defective bulbs.
Solution:
Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 6

Question 7.
A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tads.
Solution:
Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 7

Question 8
A random variable X has the following probability distribution:
NCERT Solutions for Class 12 Maths Chapter 13 Probability 8
Determine
(i) k
(ii) P(X6)
(iv) P(0
Solution:
Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 8

Question 9.
The random variable X has a probability distribution P (X) of the following form, where k is some number
NCERT Solutions for Class 12 Maths Chapter 13 Probability 9.1
(a) Determine the value of k
(b) FindP(X
Solution:
Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 9

Question 10.
Find the mean number of heads in three tosses of a fair coin.
Solution:
Maths NCERT Solutions Chapter 13 Probability Ex 13.4 Q 10

Question 11.
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 11

Question 12.
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E (X)
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 12
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 12 - i

Question 13.
Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.
Solution:
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 13
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 13 -i
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 13 -ii
NCERT Solutions for Class 12 Maths Chapter 13 Ex 13.4 Q 13 -iii

Question 14.
A class has 15 students whose ages are 14,17, 15,14,21,17,19,20,16,18,20,17,16,19 and 20 years. One student is selected in such a manner that each has the same chance of being chosen and the age X of the selected student is recorded.What is the probability distribution of the random variable X ? Find mean, variance and standard deviation of X?
Solution:
NCERT Solutions Class 12 Maths Chapter 13 Ex 13.4 Q 14
NCERT Solutions Class 12 Maths Chapter 13 Ex 13.4 Q 14 - i
NCERT Solutions Class 12 Maths Chapter 13 Ex 13.4 Q 14 - ii

Question 15.
In a meeting, 70% of the members favour and 30% oppose a certain proposal. A member is selected at random and we take X = 0, if he opposed, and X = 1, if he is in favour Find E (X) and Var (X).
Solution:
NCERT Solutions Class 12 Maths Chapter 13 Ex 13.4 Q 15
NCERT Solutions Class 12 Maths Chapter 13 Ex 13.4 Q 15 - i

Choose the correct answer in each of the following:

Question 16.
The mean of the number obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is
(a) 1
(b) 2
(c) 5
(d) (frac { 8 }{ 3 })
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.4 Q 16

Question 17.
Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. What is the value of E (X)?
(a) (frac { 37 }{ 221 })
(b) (frac { 5 }{ 13 })
(c) (frac { 1 }{ 13 })
(d) (frac { 2 }{ 13 })
Solution:
Probability Class 12 Maths NCERT Solutions Chapter 13 Ex 13.4 Q 17

We hope the given NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.4 will help you. If you have any query regarding Class 12 Maths NCERT Solutions Probability Ex 13.4, drop a comment below and we will get back to you at the earliest.

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