Probability Questions - JEE

NTA Test 14 (Single Choice) For an admission test of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is $\frac{1}{3}$, then the probability that he is unable to solve less than two problems is

$8n$ players $P_1, P_2, \ldots, P_{8n}$ play a knock out tournament. It is known that all the players are of equal strength. The tournament is held in 3 rounds where the players are paired at random in each round. If it is given that $P_1$ wins in the third round. The probability that $P_2$ looses in the second round is:

A number is chosen at random from the numbers 10 to 99. By seeing the number a man will laugh if product of the digits is 12. If he choose three numbers with replacement then the probability that he will laugh at least once is:

A determinant is chosen at random from the set of all $2 \times 2$ determinants with entries from $\{0, 1\}$. The probability that the value of the chosen determinant is positive is

In a test, an examinee either guesses or knows the answer to a multiple choice question with four choices. The probability that he makes a guess is $\frac{1}{4}$ and the probability that his answer is correct given that he guesses is $\frac{1}{4}$. The probability that his answer is correct given that he knows is $1$. The probability that he knew the answer to the question given that he correctly answered, is

The probability that in a random arrangement of the word MATHEMATICS, the two M's are not together given that the two A's are not together is

A boy comes from a family of two children. What is the probability that the other child is his sister?

Two positive real numbers $x$ and $y$ satisfying $x\leq1$ and $y\leq1$ are chosen at random. The probability that $x+y\leq1$, given that $x^2+y^2\geq\frac{1}{4}$, is

A shooter hits a target with probability $\frac{1}{4}$. She fires until she hits 3 times. Probability that she fires exactly 6 bullets lies in the interval

Mr. A's bag has 1 blue, 2 red, 1 green, 2 violet balls. Mr. B's bag has 3 red, 2 blue, 1 green ball. One ball is drawn from each bag. The probability that both balls are the same colour is

A bag contains 30 white and 10 red balls. 16 balls are drawn with replacement. Let $X$ = number of white balls drawn. The value of $\dfrac{\text{mean} + \text{S.D.}}{\text{mean} - \text{S.D.}}$ is [JEE Main 2020]

Whenever horses $A$, $B$, $C$ race together, their respective probabilities of winning are $\dfrac{1}{2}$, $\dfrac{1}{5}$, and $\dfrac{1}{4}$. If they race three times, the probability that the same horse wins all three races is

The probability that a randomly chosen 5-digit number formed by selecting 5 distinct digits from $\{1, 2, \ldots, 9\}$ is an odd number is

Neha lists all positive divisors of $(2010)^2$. She randomly selects 2 distinct divisors. Probability that exactly one is a perfect square is

A man has 3 pairs of black socks and 2 pairs of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock 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

Two different families $A$ and $B$ are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family $B$ is $1/12$, then the number of children in each family is

Balls are drawn one-by-one without replacement from a box containing 2 black, 4 white and 3 red balls till all the balls are drawn. Find the probability that the balls drawn are in the order 2 black, 4 white and 3 red.

If 10 different balls are placed in 4 distinct boxes at random, the probability that two of these boxes contain exactly 2 and exactly 3 balls is [JEE Main 2020]

A die is thrown 7 times. What is the chance that an odd number turns up (i) exactly 4 times, (ii) at least 4 times?

In binomial distribution mean = np = 2 and variance npq = 1. Then find P(x ≥ 1).

A biased coin with probability p, 0 < p < 1, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is 2/5, then p equals

A coin is tossed 7 times. Then the probability that at least 4 consecutive heads appear is

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is

In a binomial distribution $B(n,\ p = 1/4)$, if the probability of at least one success is greater than or equal to $9/10$, then $n$ is greater than

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:

Two families each having 4 members are to be seated around a circular table with alternate red and blue chairs. If probability that members of same family are seated together is $p$, then $35p$ equals

India and Pakistan is playing a best four of 7 match series. What is the probability that the tournament ends up in 6 matches assume that no match ends up in a draw?

Given three indentical bags each containing 10 balls, whose colours are as follows : Red Blue Green Bag I 3 2 5 Bag II 4 3 3 Bag III 5 1 4 A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the balls is Green, the probability that it is from bag III is q , then the value of ( 1$p + 1$q ) is :

In a game called "odd man out" $m$ ($m > 2$) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is

Two numbers $x$ and $y$ are selected at random from $[0, 1]$. The probability that $|x - y| \leq \dfrac{1}{2}$ is

Susmit met his fast friend Ricky. Susmit asked Ricky, How many children do you have? Ricky replied 2, further Ricky added that one of his son born on Sunday then what is the probability that he has two sons?

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is:

A person throws two fair dice. He wins ₹15 for throwing a doublet (same numbers on the two dice), wins ₹12 when the throw results in the sum of 9, and loses ₹6 for any other outcome on the throw. Then the expected gain/loss (in ₹) of the person is

If $X$ follows binomial distribution with $n=8$ and $p=1/2$, then $P(|X-4|\le 2)$ is

A dice is rolled three times. Find the probability of getting a larger number than the previous number each time.

A composite number is selected at random from the first 30 natural numbers and it is divided by 5. The probability that there will be a remainder is

Let P(x) denote the probability of the occurrence of event x. Plot all those points (x, y) = (P(A), P(B)) in a plane which satisfy the conditions, P(A ∪ B) ≥ 3/4 and 1/8 ≤ P(A ∩ B) ≤ 3/8. The shaded region representing the solution is bounded by which of the following?

A natural number is chosen at random from the first 100 natural numbers. The probability that $x + \dfrac{100}{x} > 50$ is

A dice is loaded so that the probability of a face $i$ is proportional to $i$, $i = 1, 2, \ldots, 6$. Then find the probability of an even number occurring when the dice is rolled.

For Problems 19–21: A player tosses a coin and scores one point for every head and two points for every tail that turns up. He plays on until his score reaches or passes $n$. $P_n$ denotes the probability of getting a score of exactly $n$.The value of $P_n + (1/2)P_{n-1}$ is equal to

For Problems 1–3: In a class of 10 students, probability of exactly i students passing an examination is directly proportional to i2. Then answer the following questions:If a student selected at random is found to have passed the examination, then the probability that he was the only student who has passed the examination is

A card is drawn from a pack of 52 cards. A person bets that it is a spade or an ace. What are the odds against him of winning this bet?

A coin is tossed 7 times. Each time a head occurs, a player wins Rs 2 and loses Rs 1 for each tail. If the player starts with Rs 0, then probability that he does NOT go negative during the game is

If the probability that the product of the outcomes of three rolls of a fair dice is a prime number is $p$, then the value of $1/(4p)$ is ________.

In a $n$-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is

Fifteen coupons are numbered 1, 2, …, 15 respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon as 9, is

There are two bags each containing 10 books all having different titles but of the same size. A student draws out books from the first bag as well as from the second bag. Find the probability that the difference between the books drawn from the two bags does not exceed 2.

For Problems 10–12: Let $S$ and $T$ are two events defined on a sample space with probabilities $P(S) = 0.5$, $P(T) = 0.69$, $P(S/T) = 0.5$.The value of $P(S \cap T)$ is

For Problems 13–15: An amoeba either splits into two or remains the same or eventually dies out immediately after completion of every second with probabilities, respectively, 1/2, 1/4, and 1/4. Let the initial amoeba be called as mother amoeba and after every second, the amoeba, if it is distinct from the previous one, be called as 2nd, 3rd, ... generations.The probability that after 2 s exactly 4 amoeba are alive is

Probability Questions (959)