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Recent questions tagged sec-b
Questions
Bag I contains 3 red and 4 black balls and Bag II contains 4 red and 5 black balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.
cbse
class12
bookproblem
ch13
misc
p584
q16
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose we have four boxes A,B,C and D containing coloured marbles as given in the box below. One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C? \[\]$\begin{matrix} \text{Box} & &\text{Marble Colour} & \\ &\text{Red} &\text{White} & \text{Black}\\ A & 1 & 6 & 3\\ B & 6 & 2 &2 \\ C & 8 & 1 & 1\\ D & 0 & 6 & 4 \end{matrix}$
cbse
class12
bookproblem
ch13
misc
p583
q12
sec-b
difficult
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.
cbse
class12
bookproblem
ch13
misc
p583
q11
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
2
answers
How many times must a man toss a fair coin so that the probability of having at least one head is more than 90%?
cbse
class12
bookproblem
ch13
misc
p583
q10
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.
cbse
class12
bookproblem
ch13
misc
p583
q9
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
cbse
class12
bookproblem
ch13
misc
p583
q7
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
cbse
class12
bookproblem
ch13
misc
p583
q6
sec-b
easy
modelpaper
2012
q21
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose that 90% of people are right-handed. What is the probability that at most 6 of a random sample of 10 people are right-handed?
cbse
class12
bookproblem
ch13
misc
p582
q4
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose that 5% of men and 0.25% of women have grey hair. A grey haired person is selected at random. What is the probability of this person being male? Assume that there are equal number of males and females.
cbse
class12
bookproblem
ch13
misc
p582
q3
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A couple has two children, (i) Find the probability that both children are males, if it is known that at least one of the children is male. (ii) Find the probability that both children are females, if it is known that the elder child is a female.
cbse
class12
bookproblem
ch13
misc
p582
q2
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The probability that a student is not a swimmer is 1 / 5. Then the probability that out of five students, four are swimmers is?
cbse
class12
bookproblem
ch13
sec5
p578
q15
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a box containing 100 bulbs, 10 are defective. What is the probability that out of a sample of 5 bulbs, none is defective?
cbse
class12
bookproblem
ch13
sec5
p578
q14
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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?
cbse
class12
bookproblem
ch13
sec5
p578
q13
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
cbse
class12
bookproblem
ch13
sec5
p578
q12
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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 (a) at least once (b) exactly once (c) at least twice?
cbse
class12
bookproblem
ch13
sec5
p577
q10
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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 ?
cbse
class12
bookproblem
ch13
sec5
p577
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Suppose X has a binomial distribution \(B\: ( 6, \frac{1}{2})\) . Show that X = 3 is the most likely outcome. Hint : P(X = 3) is the maximum among all \(P(x_i),\: x_i = 0,1,2,3,4,5,6\)
cbse
class12
bookproblem
ch13
sec5
p577
q8
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs \[ \text{ (i) none (ii) not more than one (iii) more than one (iv) at least one} \] will fuse after 150 days of use.
cbse
class12
bookproblem
ch13
sec5
p577
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?
cbse
class12
bookproblem
ch13
sec5
p577
q4
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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?
cbse
class12
bookproblem
ch13
sec5
p577
q3
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
cbse
class12
bookproblem
ch13
sec5
p577
q2
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A die is thrown 6 times. If getting an odd number is a success, what is the probability?
cbse
class12
bookproblem
ch13
sec5
p576
q1
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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).
cbse
class12
bookproblem
ch13
sec4
p571
q15
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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.
cbse
class12
bookproblem
ch13
sec4
p571
q14
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of X.
cbse
class12
bookproblem
ch13
sec4
p571
q13
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
2
answers
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).
cbse
class12
bookproblem
ch13
sec4
p571
q12
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
cbse
class12
bookproblem
ch13
sec4
p571
q11
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the mean number of heads in three tosses of a fair coin.
cbse
class12
bookproblem
ch13
sec4
p571
q10
easy
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
The random variable X has a probability distribution P(X) of the following form, where k is some number : \[ P(X) = \left\{ \begin{array}{l l} k & \quad \text{if $x$ = 0}\\ 2k & \quad \text{if $x$ = 1} \\ 3k & \quad \text{if $x$ = 2} \\ 0 & \quad \text{otherwise} \end{array} \right. \] (a) Determine the value of k. (b) Find $P (X \lt 2), P (X \leq 2), P(X \geq 2).$
cbse
class12
bookproblem
ch13
sec4
p571
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Given the following probability distribution, $\begin{matrix} \text{X} & 0 &1 &2 &3&4&5&6&7\\ \text{P(X)}&0&k&2k&2k&3k&k^2&2k^2&7k^2+k \end{matrix}$ \[\]determine $\;(i) k\quad (ii) P(X \lt 3)\quad (iii) P(X \gt 6)\quad (iv) P(0 \lt X \lt 3)$
cbse
class12
bookproblem
ch13
sec4
p570
q8
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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 tails.
cbse
class12
bookproblem
ch13
sec4
p570
q7
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
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.
cbse
class12
bookproblem
ch13
sec4
p570
q6
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as \[ \text {(i) number greater than 4 (ii) six appears on at least one die} \]
cbse
class12
bookproblem
ch13
sec4
p570
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond
cbse
class12
bookproblem
ch13
sec3
p557
q12
sec-b
medium
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability is 0.3 if the second group wins. Find the probability that the new product introduced was by the second group.
cbse
class12
bookproblem
ch13
sec3
p556
q9
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?
cbse
class12
bookproblem
ch13
sec3
p556
q8
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of an accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver? (Note, in 2014, this was modified to ask for the probability that he is a car driver also).
cbse
class12
bookproblem
ch13
sec3
p556
q7
sec-b
easy
math
modelpaper-2014
q26-a
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive ?
cbse
class12
bookproblem
ch13
sec3
p556
q5
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $ \frac{3}{4} $ be the probability that he knows the answer and $\frac{1}{4} $ be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability $ \frac{1}{4} $ . What is the probability that the student knows the answer given that he answered it correctly?
cbse
class12
bookproblem
ch13
sec3
p556
q4
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?
cbse
class12
bookproblem
ch13
sec3
p556
q3
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
cbse
class12
bookproblem
ch13
sec3
p556
q2
sec-b
medium
modelpaper
2012
q23
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?
cbse
class12
bookproblem
ch13
sec3
p555
q1
medium
sec-b
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?
cbse
class12
bookproblem
ch6
sec5
q22
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?
cbse
class12
bookproblem
ch6
sec5
q21
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
In a hostel, 60% of the students read Hindi news paper, 40% read English news paper and 20% read both Hindi and English news papers. A student is selected at random. (a) Find the probability that she reads neither Hindi nor English news papers. (b) If she reads Hindi news paper, find the probability that she reads English news paper. (c) If she reads English news paper, find the probability that she reads Hindi news paper.
cbse
class12
bookproblem
ch13
sec2
p548
q16
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square in cms to be cut off so that the volume of the box is maximum ?
cbse
class12
bookproblem
ch6
sec5
q18
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two positive numbers \(x\) and \(y\) such that their sum is 35 and the product \(x^2 y^5\) is a maximum.
cbse
class12
bookproblem
ch6
sec5
q15
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two positive numbers $x$ and $y$ such that $x + y = 60$ and $xy^3$ is maximum.
cbse
class12
bookproblem
ch6
sec5
q14
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find two numbers whose sum is 24 and whose product is as large as possible.
cbse
class12
bookproblem
ch6
sec5
q13
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Find the maximum and minimum values of \( x + \sin\: 2x\) on \([0, 2\pi].\)
cbse
class12
bookproblem
ch6
sec5
q12
p233
sec-b
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
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