Two biased dice are thrown together. For the first dice `P(6) = (1)/(2)` , the other scores being equally likely while for the second dice, `P(1) = (2)/(5)` and the other scores are equally likely. Find the probability distribution of 'the number of ones seen'.

A biased die is such that P(4) = (1)/(10) and other scores being equally likely. The die is tossed twice. If X is the 'number of fours seen', then find the variance of the random variable X.

Three six faced dice are tossed together, then the probability that exactly two of the three numbers are equal is :

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 (i0 9ii) 12.

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.

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) 3 (ii) 12.

One balanced coin is tossed. If two head comes up then two balanced dice are tossed and sum of the numbers obtained on it is noted. If tail is obtain then one card is selected from the card numbered 1 to 9 and its number is noted. Then ....... is the probability of event that noted number from card is 7 or 8.

Two dice are thrown. The number on one die is multiple of 2 and the number on other die is multiple of 3. Its probability is ......

Two dice are thrown. Find the probability that the numbers appeared has the sum 8, if it is known that the second die always exhibits 4.

Prove that the points (0, -1, -7), (2, 1, -9) and (6, 5, -13) are collinear. Find the ratio in which the first point divides the join of the other two.

A number is selected from numbers 1, 2, 3, 4 and another number is selected from numbers 1, 5, 6, 12. Find the probability that the product of two numbers selected is less than 12.