Recent questions tagged ch13

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

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

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

Ask Questions, Get Answers