On a normal standard die one of the 21 dots from any one of the six faces is removed at random with each dot equally likely to be chosen. If the die is then rolled, then find the probability that the odd number appears.

Three balls marked with 1, 2 and 3 are placed in an urn. One ball is drawn, its number is noted, then the ball is returned to the urn. This process is repeated and then repeated once more. Each ball is equally likely to be drawn on each occasion. If the sum of the number noted is 6, then the probability that the ball numbered with 2 is drawn at all the three occassion, is

A six faced die is so biased that it is twice as likely to show an even number as an odd. It is thrown twice. What is the probability that the sum of the numbers is even ?

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is i. 9 ii) 12.

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

Two digits are chosen at random from the digits 1, 2, 3, …, 9, if the sum of the chosen digits is odd, find the probability that one of the chosen digit is 6.

An urn contains 6 white and 4 black balls. A fair die whose faces are numbered from 1 to 6 is rolled and number of balls equal to that of the number appearing on the die is drawn from the urn at random. Find the probability that the balls selected are white.

A die is rolled thrice, find the probability of getting a larger number each time than the previous number.

A die has six faces numbered from 1 to 6. It is rolled and the number on the top face is noted. When this is treated as a random trial. a) What are the possible outcomes ? b)Are they equally likely? Why? c) Find the probability of a composite number turning up on the top face.

Each of the two identical bags contain 5 white and 5 red balls. One ball is transferred at random without notice from the second bag to the first bag. Then one ball is drawn from the first bag. Find the probability that the ball drawn is a red ball.

Three boxes of the same appearance have the following proportions of black and white balls : Box I-5 black and 3 white, Box II-6 black and 2 white: BoxIII-3 black and 5 white, one of the boxes is selected at random and one ball is drawn randomly from it. Given that the ball is black, find the probability that it came from Box III.