### Aptitude - Probability Test

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Two urns contain 5 white and 7 black balls and 3 white and 9 black balls respectively. One ball is transferred to the second urn and then one ball is drawn from the second urn. Find the probability that the first ball transferred is black, given that the ball drawn is black?

From 7 men and 5 ladies a committee of 4 is to be formed. If Mrs. X is not willing to join the committee in which Mr.Y is a member whereas Mr. Y is willing to join the committee only if Mrs. Z is included, how many such committees in all are possible?

In how many ways is it possible to choose a white square and a black square on a chess board so that the squares must not lie in the same row or column?

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

A number is selected at random from first thirty natural numbers. What is the chance that it is a multiple of either 3 or 13?

In how many distinguishably different ways can a cube be painted using at most two colours - White and Black - such that each face is coloured with exactly one of the two given colours?

An urn contains 6red, 5 blue and 2 green marbles. If three marbles are picked at random, what is the probability that at least one is blue?

A bag contains 21 toys numbered 1 to 21. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.

There are three cities A, B and C. Each of these cities is connected with the other two cities by at least one direct road. If a traveller wants to go from on city (origin) to another city (destination), she can do so either by traversing a road connecting the two cities directly, or by traversing two roads, the first connecting the origin to the third city and the second connecting the third city to the destination. In all there are 33 routes from A to B (including those via C). Similarly, there are 23 routes from B to C (including those via A). How many roads are there from A to C directly?

The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

The weights in kilograms of 10 students are 52, 45, 31, 35, 40, 55, 60, 38, 44, 36. If 44 is replaced by 46 and 40 is replaced by 35 then new median will be

Organising a party requires a lot of effort. In a buffet salad party, the host had 4 differentvegetables for salads. How many different salads can a guest make from the four vegetables -lettuce, cucumber, carrot, and mushrooms, if even a single vegetable is a salad ?

A set of cards bearing the number 200-299 is used in a game. if card is drawn at random, what is the probability that it is divisible by:

In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Two different teams with four students each were training for an international math contest. The students were given an assessment exam and their scores were ranked. What is the probability that the four best scores come from only one of the teams assuming that no two students got the same score?

Four cards are drawn at random from a pack of 52 plating cards. Find the probability of getting all the four cards of the same suit

Which letter is such that the difference of its integer-code with the integer-code of T is the same as that between the integer-codes of N and S?

Four unit squares are chosen at random on a chessboard. What is the probability that three of them are of one colour and fourth is of opposite colour?

A man has nine friends, four boys and five girls. In how many ways can he invite them, if there have to be exactly three girls in the invitees?

Two cards are drawn  together from a pack of 52 cards .The probability that one is a spade and one is a heart ,is

In a game there are 70 people in which 40 are boys and 30 are girls, out of which 10 people are selected at random. One from the total group, thus selected is selected as a leader at random. What is the probability that the person, chosen as the leader is a boy?

Shiwani thought of a two-digit number and divided the number by the sum of the digits of the number. He found that the remainder is 3. Devesh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Shiwani and Devesh is TRUE?

In a simultaneous throw of two coins he probability of getting at least one head is

What is the probability that a non-leap year has 53 Fridays?

A card is drawn from a pack of 52 cards .The probability of getting a queen of club or king of heart is

Three unbiased coins are tossed. What is the probability of getting at most two heads?

Let x = 3a + 3b, where a and b are chosen independently from the integers1 through 100 inclusive (with each integer having an equal likelihood of being chosen). Compute the probability that x is an integral multiple of 5.

A and B play a game where each is asked to select a number from 1 to 5. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is:

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