Recent questions in Probability

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

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

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

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

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

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

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

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

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

Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find (i) P(A $\cap$ B) (ii) P(A $\cup$ B) (iii) P ( $\large\frac{A}{B}$ ) (iv) P ( $\large\frac{B}{A}$ )

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Given that the events A and B are such that $P(A) = \large \frac{1}{2} , P (A \cap B) = \large \frac{3}{5}$ and $P(B) = p$ . Find p if they are (i) mutually exclusive (ii) independent.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Let E and F be events with $P (E) = \frac{3}{5} , P (F)= \frac{3}{10}$ and $P (E \cap F) = \frac{1}{5}$ . Are E and F independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event of the number being even, and B be the event of the number being red. Are A and B independent?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A fair coin and an unbiased die are tossed. Let A be the event - head appears on the coin and B be the event 3 on the die. Check whether A and B are independent events or not.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If $P(A) = \frac{3}{5}$ and $P(B) = \frac{1}{5}$ , find $P (A \cap B)$ if A and B are independent events.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If A and B are events such that P(A|B) = P(B|A), then which of the following is true?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

If P (A) = $\frac{1}{2}$ , P (B) = 0, what is P (A|B) ? $\begin{array} ((A) 0 \quad & (B) \frac{1}{2} \\ (C) not\: defined \quad & (D) 1 \end{array}$

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event - the coin shows a tail, given that - at least one die shows a 3.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Given that the two numbers appearing on throwing two dice are different. Find the probability of the event - the sum of numbers on the dice is 4.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl, (ii) at least one is a girl?

asked Nov 27, 2012 by balaji.thirumalai

1 answer

A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Determine P(E|F) . Mother, father and son line up at random for a family picture E : son on one end, F : father in middle

asked Nov 27, 2012 by balaji.thirumalai

1 answer

Determine P(E|F) . A die is thrown three times, E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses

asked Nov 27, 2012 by balaji.thirumalai

1 answer

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