Probability Questions - JEE

Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is:

A student appears for tests I, II and III. The student is successful if he passes in tests I, II or I, III. The probabilities of the student passing in tests I, II and III are respectively $p$, $q$ and $\frac{1}{2}$. If the probability of the student to be successful is $\frac{1}{2}$ then

A group of students comprising $3$ girls and $5$ boys went for a picnic. During a game they were arranged in a circle then the probability that each boy has one girl on at least one side is ______.

The probabilities that a student passes in Mathematics, physics and chemistry are $m, p$ and $c$, respectively. Of these subjects, the student has a $75\%$ chance of passing in at least one, a $50\%$ chance of passing in exactly two. Then $p + m + c$ is ______.

Two non-negative integers are chosen at random from the set of non-negative integers with replacement. What is the probability that the sum of their squares is divisible by 10?

A fair coin is tossed 5 times. Find the probability that no two consecutive heads occur.

The probability that a teacher will give a surprise test during any class meeting is $\frac{1}{5}$. If a student is absent twice, then the probability that the student will miss at least one test is

If $A$ and $B$ are two events such that $P(A) = 0.3, P(B) = 0.25, P\left(A \cap B\right) = 0.2$, then $10P\left(\frac{A^C}{B^C}\right)$ is equal to ______.

A number is selected at random from the first twenty-five natural numbers. If it is a composite number, then it is divided by $5$. But if it is not a composite number, it is divided by $2$. The probability that there will be no remainder in the division is ______.

$A$ speaks truth $3$ times out of $4$, and $B$ $7$ times out of $10$, they both assert that a white ball has been drawn from a bag containing $6$ balls all of different colours; the probability of truth of the assertion is ______.

The probability of India winning a test match against West Indies is 1/2 assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is:

Consider 5 independent Bernoulli's trials each with probability of success $p$. If the probability of at least one failure is greater than or equal to $\dfrac{31}{32}$, then $p$ lies in the interval

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are $3/4$, $1/2$ and $5/8$, respectively, then the probability that the target is hit by P or Q but not by R is:

Sixteen players $S_1, S_2, S_3, \ldots, S_{16}$ play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players of the pair. Assume that all the players are of equal strength.(a) Find the probability that the player $S_1$ is among the eight winners.(b) Find the probability that exactly one of the two players $S_1$ and $S_2$ is among the eight winners.

A box '$A$' contains 2 white, 3 red and 2 black balls. Another box '$B$' contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box '$B$' is

Whenever horses $a$, $b$, $c$ race together, their respective probabilities of winning the race are 0.3, 0.5, and 0.2, respectively. If they race three times, the probability that the same horse wins all the three races, and the probability that $a$, $b$, $c$ each wins one race are, respectively

If $P(A) = \frac{2}{3}$, $P(B) = \frac{1}{2}$ and $P(A \cup B) = \frac{5}{6}$ then the events $A$ and $B$ are

Football teams T1 and T2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T1 winning, drawing and losing a game against T2 are $\frac{1}{2}$, $\frac{1}{6}$ and $\frac{1}{3}$ respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T1 and T2 respectively, after two games. Find $P(X = Y)$.

Choosing {x, y, z} ⊂ S, such that x, y, z are in AP, is

Choosing {x, y, z} ⊂ S, such that x, y, z are not consecutive, is

$P(E_1 \cap E_2) + P(E_2 \cap E_3) + P(E_3 \cap E_1)$ equals

Three-digit numbers are formed using the digits 0, 1, 2, 3, 4, 5 without repetition of digits. If a number is chosen at random, then the probability that the digits either increase or decrease, is

The probability that roots of the quadratic equation $ax^2 + bx + c = 0$ are imaginary, is

Which of the following statement is false?(a) A and B are mutually exclusive(b) A and B are mutually exclusive and exhaustive(c) $A = B'$(d) A and C are mutually exclusive

The probability that at least one of the events A and B occurs is $\frac{3}{5}$. If A and B occur simultaneously with probability $\frac{1}{5}$, then $P(A) + P(B)$ is

A fair coin is tossed repeatedly. If the tail appears on first four tosses, then the probability of the head appearing on the fifth toss is equal to

If the papers of 4 students can be checked by any one of the 7 teachers. If the probability that all the 4 papers are checked by exactly 2 teachers is A, then the value of $490A$ must be ……….

A fair six-faced die is rolled 12 times. The probability that each face turns up twice is equal to

If the probability that E or F happens is 1 and the probability that neither E nor F happens is $\frac{1}{2}$, then find $P(E)$ and $P(F)$

Four fair dice D1, D2, D3 and D4 each having six faces numbered 1, 2, 3, 4, 5 and 6 are rolled simultaneously. The probability that D4 shows a number appearing on one of D1, D2 and D3 is

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. A fair die is thrown three times. If $r_1, r_2$ and $r_3$ are the numbers obtained on the die, then the probability that $\omega^{r_1} + \omega^{r_2} + \omega^{r_3} = 0$ is

A lot contains 20 articles. The probability that the lot contains exactly 2 defective articles is 0.4 and the probability that the lot contains exactly 3 defective articles is 0.6. Articles are drawn from the lot at random one by one without replacement and are tested till all defective articles are found. What is the probability that the testing procedure ends at the twelfth testing?

Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and 0.2048 respectively. Then, the probability of getting exactly 3 successes is equal to

Let $E_C$ denote the complement of an event E. Let $E_1, E_2$ and $E_3$ be any pairwise independent events with $P(E_1) > 0$ and $P(E_1 \cap E_2 \cap E_3) = 0$. Then $P(E_2^C \cap E_3^C | E_1)$ is equal to

Let $S$ be a set of 5 elements and $P(S)$ denote the power set of $S$. Let $E$ be an event of choosing an ordered pair $(A,B)$ from $P(S)\times P(S)$ such that $A\cap B=\emptyset$. If the probability of the event $E$ is $\dfrac{p}{2^q}$, where $p,q\in\mathbb{N}$, then $p+q$ is equal to _____.

A bag contains 5 white and 3 black balls. 4 balls are successively drawn out and not replaced. What is the probability that they are alternately of different colours?

Five different marbles are placed in 5 different boxes randomly. Then the probability that exactly two boxes remain empty is (each box can hold any number of marbles)

A $2n$ digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consecutive digits of the number is prime is

When a missile is fired from a ship, the probability that it is intercepted is $\frac{1}{3}$ and the probability that the missile hits the target, given that it is not intercepted, is $\frac{3}{4}$. If three missiles are fired independently from the ship, then the probability that all three hit the target, is

A pair of numbers is picked up randomly (without replacement) from the set {1, 2, 3, 5, 7, 11, 12, 13, 17, 19}. The probability that the number 11 was picked given that the sum of the numbers was even is nearly

The probability that a year chosen at random has 53 Sundays, is

260. The probability of occurrence of a multiple of 2 on one dice and a multiple of 3 on the other dice if both are thrown together, is:

Numbers from {1..10}. Prob min=3 or max=7.

Let a die is loaded in such a way that prime number faces are twice as likely to occur as a non-prime number faces. Then, the probability that an odd number will be show up when the die is tossed, is

A bag contains Red balls and Black balls such that $4R + 6B = 10$. Two balls are drawn at random. If $P$ is the probability that one ball is Red and one ball is Black, then $P$ equals:

A couple has two children. It is known that at least one of the children is a boy born on Sunday. What is the probability that both children are boys?

The probability that Krishna will be alive 10 years hence is 7/15 and that Hari will be alive is 7/10. What is the probability that both Krishna and Hari will be dead 10 years hence?

If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7 is

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. Find the probability that the determinant chosen is non-zero.

An urn contains 3 red balls and $n$ white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is 1/2. Mr. B draws one ball from the urn, notes its color and replaces it. He then draws a second ball from the urn and finds that both balls have the same color is 5/8. The possible value of $n$ is

Probability Questions (959)