Recent questions tagged bookproblem

The mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is

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).

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.

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.

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).

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.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find the mean number of heads in three tosses of a fair coin.

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 $P (X \lt 2), P (X \leq 2), P(X \geq 2).$

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 $\;(i) k\quad (ii) P(X \lt 3)\quad (iii) P(X \gt 6)\quad (iv) P(0 \lt X \lt 3)$

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.

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.

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 \[ \text {(i) number greater than 4 (ii) six appears on at least one die} \]

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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 ?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

State which of the following is a probability distributions of a random variable. Give reasons for your answer.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If A and B are two events such that $A ⊂ B$ and $P(B) ≠ 0$, then which of the following is correct?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Probability that A speaks truth is $\large \frac{4}{5} $ . A coin is tossed. A reports that a head appears. The probability that actually there was head is?

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

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is $ \sin^{-1} \left(\frac{1}{3}\right)$

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4, she tosses a coin once and notes whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 or 4 with the die?

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.

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?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is $\tan^{-1} \sqrt {2}$.

asked Nov 27, 2012 by thanvigandhi_1

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).

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 ?

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?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that the right circular cone of least curved surface and given volume has an altitude equal to $\sqrt 2$ time the radius of the base.

asked Nov 27, 2012 by thanvigandhi_1

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?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is$\large\frac{8}{27}$ of the volume of the sphere.

asked Nov 27, 2012 by thanvigandhi_1

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.

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?

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?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Two events A and B will be independent, if which of the following is true?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Choose the correct answer: The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

asked Nov 27, 2012 by balaji.thirumalai

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?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

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.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

One card is drawn at random from a well shuffled deck of 52 cards. Are E and F independant if: E : the card drawn is a spade F : the card drawn is an ace

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Probability of solving specific problem independently by A and B are $\large \frac{1}{2} $ and $\large \frac{1}{3} $ respectively. If both try to solve the problem independently, find the probability that $ \text {(i) the problem is solved (ii) exactly one of them solves the problem.} $

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 ?

asked Nov 27, 2012 by thanvigandhi_1

1 answer

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A die is tossed thrice. Find the probability of getting an odd number at least once.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Events A and B are such that $P (A) = \frac{1}{2} , P(B) = \frac{7}{12}$ and P(not A or not B) = $ \frac{1}{4} $ . State whether A and B are independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.

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.

asked Nov 27, 2012 by thanvigandhi_1

1 answer

If A and B are two events such that $P (A) = \large \frac{1}{4} , P (B) = \large\frac{1}{2} $ and $P(A \cap B) = \large \frac{1}{8} $ , find $P$ (not A and not B).

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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