On a normal standard dic one of the 21 dots from any one of the six faccs is removéd at random with each dot equally likely to be chosen. The die is then rolled. The probability that the top face has an odd number of dots is

A box cantains 30 tickets, bearing only one number from 1 to 30 on each. If one ticket is drawn at random, find the probability of an event that the ticket drawn bears an odd number

A purse contains 2 six-sided dice. One is a normal fair die, while the other has two 1s two 3s,and two 5s. 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 dice is rolled and shows up the face 3. The probability that a fair die was picked up is (a) 1/7 (b) 1/4 (c) 1/6 (d) 1/24

Mr. A lives at origin on the Cartesian plane and has his office at (4,5) His friend lives at (2,3) on the same plane. Mrs. A can go to his office travelling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considere (a) 1/2 (b) 10/21 (c) 1/4 (d) 11/21

four fair dice D_1, D_2,D_3 and D_4 each having six faces numbered 1,2,3,4,5 and 6 are rolled simultaneously. The probability that D_4 shows a number appearing on one of D_1,D_2,D_3 is

A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19 and 20 years. One student is selected such a manner that each has the same chance of being chosen and the age X of the selected student is recorded. What is the probability distribution of the random variable X? Find mean, variance and standard deviation of X.

There are two die A and B both having six faces. Die A has three faces marked with 1, two faces marked with 2, and one face marked with 1, two faces marked with 2, and one face marked with 3. Die B has one face marked with 1, two faces marked with 2, and three faces marked with 3. Both dices are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and let P(E) be the probability of event E, then When x = 4, then P(E) is equal to

There are two die A and B both having six faces. Die A has three faces marked with 1 , two faces marked with 2 , and one face marked with 3 . Die B has one face marked with 1 , two faces marked with 2 , and three faces marked with 3 . Both dices are thrown randomly once. If E be the event of getting sum of the numbers appearing on top faces equal to x and let P(E) be the probability of event E , then P(E) is maximum when x equal to

Write sample space 'S' and number of sample point n(S) for each of the following experiments Also write evets A,B, C in the set form and write n(A), n(B), m( C). One die is rolled, Event A: Even number on the upper face. Event B: Odd number on the upper face. Event C: Prime number on the upper face.

There are two bags, one of which contains 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A fair die is cast, if the face 1 or 3 turns up, a ball is taken from the first bag, and if any other face turns up a ball is chosen from the second bag. Find the probability of choosing a black ball.

Column I, Column II Four dice (six faced) are rolled. The number of possible out comes in which at least one dice shows 2 is, p. 210 Let A be the set of 4-digit number a_1a_2a_3a_4w h e r ea_1> a_2> a_3> a_4dot then n(A) is equal to, q. 750 The total number of three-digit numbers, the sum of whose digits is even, is equal to, r. 671 The number of four-digit numbers that can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 so that each number contains digit 1 is, s. 450