Probability Questions - JEE

An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown $n$ times and the list of $n$ numbers shown up is noted. Then find the probability that among the numbers 1, 2, 3, 4, 5, 6 only three numbers appear in this list and each number appears at least once.

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is __________ (up to four decimal places).

Three critics review a book. Odds in favor of the book are 5:2, 4:3, and 3:4, respectively, for the three critics. The probability that majority are in favor of the book is

A class consists of 80 students, 25 of them are girls and 55 are boys. If 10 of them are rich and the remaining are poor and also 20 of them are intelligent, then the probability of selecting an intelligent rich girl is

$A$ speaks truth in 60\% cases and $B$ speaks truth in 70\% cases. The probability that they will say the same thing while describing single event is:

Let $A$ and $B$ be two events such that $P(A \cap B') = 0.20$, $P(A' \cap B) = 0.15$, $P(A' \cap B') = 0.1$, then $P(A/B)$ is equal to

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

Three factories A, B and C produce the same product. The factory A produces twice as many as B produces while the factories B and C produce in the same quantity. It is known that 2% of the products of A as well as C are defective while 4% of the products of B are defective. All the products of the three factories are stocked together. If a product is selected at random from the stock, what is the probability that the product is defective?

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, …, 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is:

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 spades. Find the probability of the missing card to be a spade.

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $P(A \cup B)$ is

The probability distribution of a random variable $X$ is given as | $X$ | $-5$ | $-4$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | $P(X)$ | $p$ | $2p$ | $3p$ | $4p$ | $5p$ | $7p$ | $9p$ | $10p$ | $11p$ | $12p$ | Then, the value of $p$ is

Four fair dices are thrown simultaneously. Find the probability that the highest number obtained is 4.

$2n$ boys are randomly divided into two subgroups containing $n$ boys each. The probability that the two tallest boys are in different groups is

For three events $A$, $B$ and $C$,$P(\text{Exactly one of } A \text{ or } B \text{ occurs})$$= P(\text{Exactly one of } B \text{ or } C \text{ occurs})$$= P(\text{Exactly one of } C \text{ or } A \text{ occurs}) = \dfrac{1}{4}$ and$P(\text{All the three events occur simultaneously}) = \dfrac{1}{16}$.Then the probability that at least one of the events occurs, is

An urn contains nine balls of which three are red, four are blue, and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

If the events $A$ and $B$ are mutually exclusive events such that $P(A) = \dfrac{3x+1}{3}$ and $P(B) = \dfrac{1-x}{4}$, then the set of possible real values of $x$ lies in the interval

Let $A$, $B$, and $C$ be three events, which are pair-wise independent and $\bar{E}$ denotes the complement of an event $E$. If $P(A \cap B \cap C) = 0$ and $P(C) > 0$, then $P[(\bar{A} \cap \bar{B}) \mid C]$ is equal to

If \(0

A 5-digit number is formed without repetition using the digits 0, 1, 2, 3, 4. The probability that the number is divisible by 4 is

A dice is weighted such that the probability of rolling the face numbered $n$ is proportional to $n^2$ ($n = 1, 2, 3, 4, 5, 6$). The dice is rolled twice, yielding the numbers $a$ and $b$. The probability that \(a

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 (that is, 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?

$P(\text{none of } E_1, E_2, E_3)$ equals

If two different numbers are taken from the set $\{0, 1, 2, 3, \ldots, 10\}$, then the probability that their sum as well as absolute difference are both multiple of 4, is [JEE Main 2017, 4M]

Follow up on ball draw.

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one with replacement, then the variance of the number of green balls drawn is [JEE Main 2017, 4M]

16. There are two bags X and Y. X contains 3 white balls and 2 black balls, and Y contains 2 white balls and 4 black balls. A bag and a ball out of that bag are picked at random. The probability that the ball is white, is ___.

For three events A, B and C, denote:P(Exactly one of A or B or C occurs) = $P_1$P(Exactly one of B or C occurs) = $P_2$P(Exactly one of C or A occurs) = $P_3$P(All the three events occur simultaneously) = $\frac{1}{16}$If $P_1 = P_2 = P_3 = \frac{1}{4}$, then the probability that at least one of the events occurs, is [JEE Main 2017, 4M]

If $E$ and $F$ are independent events such that \(0

The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these vertices is equilateral, is

One Indian and four American men and their wives are to be seated randomly around a circular table. Then, the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife, is

If three integers are selected from the set of the first 20 natural numbers, the probability that their product is a multiple of 3, is

Five different games are to be distributed among four children randomly. The probability that each child get at least one game is $p$, then the value of $[1/p]$ is, where $[\cdot]$ represents the greatest integer function ________.

Four persons hit a target with respective probabilities $\dfrac{1}{2},\dfrac{1}{3},\dfrac{1}{4},\dfrac{1}{8}$ independently. The probability that the target is hit by exactly one person is [JEE Main 2019]

If C and D are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among the following is

A and B are two candidates seeking admission to IIT. The probability that A is selected is 0.5 and the probability that A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.9?

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is __________.

In a bulb manufacturing company probability that a bulb is defective is 0.01. The company sells the bulbs in a package of 10. After getting complains about defective bulb company decided to offer a money back guarantee that at most of the 10 from the package is defective. What percentage of the packages company has to replace?

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in AP with positive common difference, is

Class XII has sections A (40%) and B (60%). 20% students get into IIT. $P$(IIT from A)$=5P$(IIT from B). A student not selected in IIT is chosen. Probability he is from section B is

In an entrance test, there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then find the probability that he was guessing.

A purse contains 2 six-sided dice. One is a normal fair die, while the other has two 1's, two 3's, and two 5's. A die is picked up and rolled. Because of some secret magnetic attraction of the unfair die, there is 75% chance of picking the unfair die and a 25% chance of picking a fair die. The die is rolled and shows up the face 3. The probability that a fair die was picked up is

There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. When one of the three coins is chosen at random and tossed, it showed heads. What is the probability that it was the two-headed coin?

Two integers are selected at random from the set $\{1, 2, \ldots, 11\}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is

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 test bank, what is the probability that it will be an easy question given that it is a multiple choice question?

A and B stand in ring along with 10 other persons. If the arrangement is at random, the probability that there are exactly 3 person between A and B, is

In a multiple choice question there are four alternative answers of which one or more than one is correct. A candidate will get marks on the question only if he ticks the correct answer. The candidate decides to tick answers at random. If he is allowed up to three chances of answer the question, then the probability that he will get marks on it is

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

Eight players $P_1, P_2, \ldots, P_8$ play a knock-out tournament. It is known that whenever the players $P_i$ and $P_j$ play, the player $P_i$ will win if \(i

Probability Questions (959)