" A die is thrown two times."

Describe the sample space for the following indicated experiments A die is thrown tow times.

A fair die is thrown two times. Find the probability that : Product of numbers on them is 12.

A fair die is thrown two times. Find the probability that : Sum of the numbers on them is 5.

A fair die is thrown two times. Find the probability that : Sum of the numbers on them is at least 8.

A fair die is thrown two times. Find the probability that : First throw gives a multiple of 2 and second throw gives a multiple of 3.

In part (ii), For a loaded die,the probabilities of outcomes are given as under :P(1)=P(2)=P(3)=P(4)=P(5)=P(6)=1/6.the die is thrown two times.Let A and B be the events, same number each times, and a total score is 10 or more, respectively.Determine if the dice were fair, whether or not the events A and B would be independent.

For a loaded die, the probabilities of outcomes are given as under : P(1) = P(2) = 0.2, P(3) = P(5) = P(6) = 0.1 and P(4) = 0.3. The die is thrown two times. Let A and B be the events, 'same number each time', and 'a total score is 10 or more', respectively. Determine whether or not A and B are independent.