In rolling a die .
Does the first player have a greater chance of getting a six on the top face?

In rolling a die . Would the player who played after him have a lesser chance of getting a six on the top face?

In rolling a die . Suppose the second player got a six on the top face. Does it mean that the third player would not have a chance of getting a six on the top face?

A candidate is selected for interview for three posts. For the first post there are 3 candidates, for the second there are 4 and for the third there are 2. What are the chances of his getting at least one post ?

A die is thrown three times, if the first throw is a four, find the chance of getting 15 as the sum.

A die thrown twice. If A is the event of getting a multiple of three in first through and B is the event of getting a sum less than 8 in two throws, then P(A//B) =

In hexagonal systems of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons and three atoms are sandwiched in between them. A space-filling model of this structure, called hexagonal close-packed (HCP), is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed over the first layer so that they touch each other and represent the second layer. Each one of these three spheres touches three spheres of the bottom layer. Finally, the second layer is covered with a third layer that is identical to the bottom layer in relative position. Assume radius of every sphere to be ‘r’. The volume of this HCP unit cell is

In the random rxperiment of rolling an unbiased die, let A be the event of getting a digit less than 4 and B be then event of getting a digit greater than 3 , show that the events A and B are mutually exclusive and exhaustive.

In a game, a man wins Rs 100 if he gets 5 or 6 on a throw of a fair die and loses Rs 50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is: