Recent questions tagged bookproblem

Construct the truth tables for the following statement :p ∨ (∼ q)

asked Nov 27, 2012 by balaji.thirumalai

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Write negation of the each of the following statements :

asked Nov 27, 2012 by balaji.thirumalai

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If p stands for the statement “Sita likes reading” and q for the statement “Sita likes playing’ what does ∼p ∧ ∼ q stand for?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Translate each of the following compound statements into symbolic form:

asked Nov 27, 2012 by balaji.thirumalai

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Let p be “Kamala is going to school” and q be “There are twenty students in the class “. Give a simple verbal sentence which describes each of the following statements : (i) p ∨ q (ii) p ∧ q (iii) ∼ p (iv) ∼ q (v) ∼p ∨ q

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Form the conjunction and the disjunction of (i) p : Anand reads newspaper, q : Anand plays cricket. (ii) p : I like tea. q : I like ice-cream.

asked Nov 27, 2012 by balaji.thirumalai

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Find out which of the following sentences are statements and which are not? Justify your answer

asked Nov 27, 2012 by balaji.thirumalai

0 answers

Write down the truth value (T or F) of the following statements

asked Nov 27, 2012 by balaji.thirumalai

1 answer

The maximum value of $ [ x(x-1) +1]^{\frac{1}{3}}, 0 \leq \: x \leq$ is

asked Nov 27, 2012 by thanvigandhi_1

1 answer

For all real values of $x$, the minimum value of $ \large\frac{1-x+x^2}{1+x+x^2}$ is

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the point on the curve $ x^2 = 2y$ which is nearest to the point $(0, 5)$ is

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Number of binary operations on the set $\{a, b\}$ are

asked Nov 27, 2012 by vaishali.a

1 answer

Let $f : R \to R$ be the Signum Function defined as \[ f(x) = \left \{ \begin {array} {1 1} 1, & \quad \text { x $>$ 0} \\ 0, & \quad \text { x $=$0} \\-1, & \quad \text { x $<$0} \\ \end {array} \right. \] and $g:R \to R$ be the greatest Integer Function given by $g(x)=[x]$ where $[x]$ is a greatest integer less thar or equal to $x$ Then, does $fog$ and $gof$ coincide in $(0,1]$?.

asked Nov 27, 2012 by vaishali.a

1 answer

Let $A = \{1, 2, 3\}$. Then number of equivalence relations containing $(1, 2)$ is

asked Nov 27, 2012 by vaishali.a

1 answer

Let $ A = \{1, 2, 3\}$. Then number of relations containing $(1, 2)\;$ and $\;(1, 3)$ which are reflexive and symmetric but not transitive is

asked Nov 27, 2012 by vaishali.a

1 answer

If A and B are any two events such that $P(A) + P(B) - P(A \text{and} B) = P(A)$, then choose the correct answer:

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If P(A|B) > P(A), then which of the following is correct ?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If A and B are two events such that P(A) $\neq$ 0 and P(B | A) = 1 . Then choose the correct answer.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An electronic assembly consists of two subsystems, say, A and B. From previous testing procedures, the following probabilities are assumed to be known: $ \text {P(A fails) = 0.2 P(B fails alone) = 0.15 P(A and B fail) = 0.15}$. Evaluate the following probabilities \[ \text {(i) P(A fails | B has failed) (ii) P(A fails alone)} \]

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability $\frac{1}{2}$).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Assume that the chances of a patient having a heart attack is 40%. It is also assumed that a meditation and yoga course reduce the risk of heart attack by 30% and prescription of certain drug reduces its chances by 25%. At a time a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga?

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? \[\]$\begin{matrix} \text{Box} & &\text{Marble Colour} & \\ &\text{Red} &\text{White} & \text{Black}\\ A & 1 & 6 & 3\\ B & 6 & 2 &2 \\ C & 8 & 1 & 1\\ D & 0 & 6 & 4 \end{matrix}$

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.

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%?

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.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?

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.

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?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An urn contains 25 balls of which 10 balls bear a mark 'X' and the remaining 15 bear a mark 'Y'. A ball is drawn at random from the urn, its mark is noted down and it is replaced. If 6 balls are drawn in this way, find the probability for the following: (i) all will bear 'X' mark. (ii) not more than 2 will bear 'Y' mark. (iii) at least one ball will bear 'Y' mark. (iv) the number of balls with 'X' mark and 'Y' mark will be equal.

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?

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.

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.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A and B are two events such that P (A) $\neq$ 0. Find P(B|A), if (i) A is a subset of B (ii) A $\cap$ B = $\phi$

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?

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?

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?

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.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the probability of getting 5 exactly twice in 7 throws of a die.

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?

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 ?

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 $P(x_i),\: x_i = 0,1,2,3,4,5,6$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers TRUE; if it falls tails, he answers FALSE. Find the probability that he answers at least 12 questions correctly.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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?

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.

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?

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?

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.

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?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is ?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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