A die is loaded so that the probability of a face i is proportional to i ,i=1,2,... 6. Then find the probability of an even number occurring when the die in rolled.

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 porbability that the odd number appears.

(a) Write the probability of getting each number on the top face when a die was rolled in the following table. (b) Find the sum of the probabilities of all outcomes.

An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on two faces is noted. If the result is a tail, a card from a well-shuffled pack of 11 cards numbered 2, 3, 4, ..., 12 is picked and the number on the card is noted. What is the probability that the noted number is either 7 or 8?

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 spinner was spun 1000 times and the frequency of outcomes was recorded as in given table: Find (a) List the possible outcomes that you can see in the spinner (b) Compute the probability of each outcome. (c) Find the ratio of each outcome to the total number of times that the spinner spun (use the table)

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

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 minimum when x equals to

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.

An unbiased dice, with faces numbered 1,2,3,4,5,6, is thrown n times and the list of n numbers shown up is noted. Then find the probability that among the numbers 1,2,3,4,5,6 only three numbers appear in this list.