A speaks the truth 5 out of 7 times and B speaks the truth 8 out of 9 times. What is the probability that they contradict each other in stating the same fact?

If A and B events with P(A) = \(\frac{3}{8}\), P(B) = \(\frac{1}{2}\) and P(A ∩ B) = \(\frac{1}{4}\). Find P(A̅ ∩ B̅).

Three cards are drawn one after another with replacements from a pack of cards. What is the probability of getting first card a Jack, second card a black card, and third card an even-numbered card?

If \(P(A \cup B) = \frac{5}{9}, P(\bar{A}\cup \bar{B})=\frac{13}{27}, P(A) = \frac{11}{18}\), then the odds against event B are:

The probabilities of solving a problem by three students A, B, and C are 3/7, 5/9, and 1/5 respectively. The probability that the problem will be solved is: 

A person can hit a target 5 times out of 8 shots. If he fires 10 shots, what is the probability that he will hit the target twice?

Sudarsan and Abraham appear for an interview for two vacancies. The probability of Sudarsan's selection is \(\frac{1}{3}\) and that of Abraham's selection is \(\frac{1}{5}.\) Find the the probability that none of them will be selected.

Two cards are drawn from the pack of 52 cards. What is the probability of getting either an ace of diamond or a queen of spade?

Two dice are thrown randomly. Find the probability of getting the sum is 4.

A glass jar contains 6 white, 8 black, 4 red, and 3 blue marbles. If a single marble is chosen at random from the jar, what is the probability that it is black or blue?

Out of 8 men and 5 women, a committee of 3 persons is to be formed. In how many ways can it be formed by selecting at least 2 women?

There are 9 fans in a hall and each one of them can be switched on independently. Find the total number of ways in which the hall can get air?
 

How many different words can be formed with the letter of the word “REGRESSIVE”

There are 6 bulbs in a room and each one of them can be switched on independently. Find the total number of ways in which the room can be illuminated?

Find the no. of way to arrange the letters of word ‘ EDUCATION ’

Three fan companies M, N, and O launched 5, 6, and 6 different models respectively. Find the ways in which they can be displayed in a case with 18 slots such that the models of no two companies are mixed together.

The number of ways in which 4 different toys can be put in two boxes of different sizes so that no box remains empty is -

How many numbers of five-digit can be formed with the digits 0, 2, 4, 5, and 7 (repetition of digits is not allowed)?

There are five different bags. Also, there are five different coins. In how many ways can the coins be put into bags?

Kishan and Bhavya appear in an interview for a vacancy. The probability of Kishan’s selection is 1/8 and that of Bhavya’s selection is 1/9. What is the probability that only one of them will be selected?

In how many ways a committee, consisting of 8 men and 6 women can be formed from 12 men and 12 women?

Quantity A: Probability of getting at least 1 prime number on dice. Two dice are thrown.

Quantity B: Ratio of the quantity of cheaper apples to total apples. Apples of Rs 22.8 per kg are mixed with Rs 28.4 per kg. The mixture is sold at 8% profit at Rs 27.54 per kg.

Quantity A : If we form all possible 4-digit numbers from 0, 2, 3, 5, and 8, and these numbers are arranged in ascending order, then what will be the rank of 3580? (repetition of digits not allowed)

Quantity B : If we form all possible Five digit numbers from 0, 2, 3,5, and 8, then in how many numbers 2 comes before 8? (repetition of digits not allowed)

Quantity A : In an interview, the probability of A to get selected is 0.6, for B to get selected is 0.8 and for C to get selected is 0.5, Find the probability of at least 2 of them having to be selected.

Quantity B : A box contains tickets numbered 1 to 16. 3 tickets are chosen at random, what is the probability that at least 2 of them contain a number which is a multiple of 5.

4 boys and 8 men are to be seated in a row on 12 chairs in such a way that all 4 men always sit together. In how many different ways can it be done?

2 tetrahedrons numbered 1 to 4 are thrown. Find the probability that the sum of numbers at the base of these tetrahedrons is more than or equal to 5.

Find the number of different ways of forming a committee consisting of 5 men and 4 women from 9 men and 7 women.

How many 2-letter words, with or without meaning, may be constructed from the letters in the word 'MEMORIALS' if letter repetition is not permitted?

There are 4 Red, 2 Green & 2 Blue ball in a bag. If one ball drawn at random from the bag, then find the probability of the ball drawn out is not blue?

In how many ways can be letters of the word ‘LIPSTICK’ be arranged?

8 men are to be seated on a bench. In how many ways can it be done if the youngest man always sits in the middle?

In how many different ways can a group of 6 men and 6 women be formed out of 10 men and 9 women?

How many words can be formed by using all the letters of the word ‘MAHAAN’?

Balls numbered 1 to 120 are kept in a basket. What is the probability that the drawn ball has a number which is multiple of 3 or 5?

A shop sells 10 bulbs out of which 3 are defective. Shyam buys four bulbs. Find the probability that at least two of the bulbs that he buys are working.

A box contains 7 pink, 5 white, and 8 yellow balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colors.

Find the probability of selecting 2 vowels (Repetition not allowed) from the given word 'PALAEONTOLOGY'.

Everybody in the room shakes hands with everybody else. The total number of hand-shakes is 91. The total number of persons in the room is:
 

Six different erasers and three boxes are taken. Each eraser is to be put in one of these boxes. No box should remain empty and all the boxes should not have the same number of erasers. In how many ways can this be done?

Quantity I: Two dice are thrown simultaneously, 1^st die shows up 4, what is the probability of sum of digits shown by the two dice being 8?

Quantity II: Two dice are thrown simultaneously, such that each of them always end up getting even number. What is the probability of sum of digits shown by the two dice being 8?

Quantity III: Two dice are thrown simultaneously. Find the probability that the sum of digits shown on both dice is more than 4 and less than 9. 

A card is drawn at random from a well-shuffled pack of 52 cards. What is the probability of getting a two of hearts or a two diamonds?

In how many ways a KHO-KHO team of 8 players can be made from 18 players if 2 particular players are never chosen?

In how many different ways can 2 pens and 3 pencils be selected from 4 pens and 10 pencils?

Dice with numbers from 1 to 6 on its faces is thrown. If the outcome is an even number, it is thrown again, otherwise not. It is known that the dice were thrown 8 times following this condition. In how many cases can the sum of numbers obtained in 8 throws be 28?

A box contains 6 pink, 5 white, and 4 yellow balls. Five balls are drawn at random. Find out the number of ways of selecting the balls such that 2 pink balls, 1 white and 2 yellow colors are drawn.

In how many ways a football team of 11 players can be made from 23 players if a particular player is never chosen?

If Sandeep rolled two dices at the same time then what is the probability of getting a sum of 9 or more than 9 on the dices?

In how many different ways can the letters of the word ‘SHIZUKA’ be arranged?

How many 3 digit numbers can be formed from the numbers 2, 4, 5, 6, 7, and 8, which are divisible by 2 and none of the digits is repeated?

In how many ways can an animal trainer arrange 4 cows and 5 dogs in a row so that no two dogs are together?