Recent questions tagged easy

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

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

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

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 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

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

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

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

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

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 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

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

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

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