The game Miljoenenjacht, which originally began in the Netherlands, is more widely known as Deal or No Deal. In the game, there are $26$ boxes, each with a different amount of money in it. At the beginning of the game, the player chooses one box which he/she hopes has the highest prize, $€ 5$ million. During the rest of the game, the player chooses boxes from those that remain. With each selection, the player knocks that box and the amount inside it off the game board. The amounts in the boxes are shown in the table at the top of the next page. 

 

$€ 0.01$	$€ 10,000$
$€ 0.20$	$€ 25,000$
$€ 0.50$	$€ 50,000$
$€ 1$	$€ 75,000$
$€ 5$	$€ 100,000$
$€ 10$	$€ 200,000$
$€ 20$	$€ 300,000$
$€ 50$	$€ 400,000$
$€ 100$	$€ 500,000$
$€ 500$	$€ 750,000$
$€ 1,000$	$€ 1,000,000$
$€ 2,500$	$€ 2,500,000$
$€ 5,000$	$€ 5,000,000$

With a contestant's initial selection of a box, find the following probabilities:

P($€ 0$)

The game Miljoenenjacht, which originally began in the Netherlands, is more widely known as Deal or No Deal. In the game, there are $26$ boxes, each with a different amount of money in it. At the beginning of the game, the player chooses one box which he/she hopes has the highest prize, $€ 5$ million. During the rest of the game, the player chooses boxes from those that remain. With each selection, the player knocks that box and the amount inside it off the game board. The amounts in the boxes are shown in the table at the top of the next page. 

After a few rounds, only the boxes below remain.

Find the following probabilities related to the next box selected:

 P(the $€ 5$ million is left on the board)

Write the answer up to $2$ decimal place.

The game Miljoenenjacht, which originally began in the Netherlands, is more widely known as Deal or No Deal. In the game, there are $26$ boxes, each with a different amount of money in it. At the beginning of the game, the player chooses one box which he/she hopes has the highest prize, $€ 5$ million. During the rest of the game, the player chooses boxes from those that remain. With each selection, the player knocks that box and the amount inside it off the game board. The amounts in the boxes are shown in the table at the top of the next page. 

After a few rounds, only the boxes below remain.

Find the following probabilities related to the next box selected:

P(the $€ 5$ million box is opened)

Write the answer up to $3$ decimal place.

The game Miljoenenjacht, which originally began in the Netherlands, is more widely known as Deal or No Deal. In the game, there are $26$ boxes, each with a different amount of money in it. At the beginning of the game, the player chooses one box which he/she hopes has the highest prize, $€ 5$ million. During the rest of the game, the player chooses boxes from those that remain. With each selection, the player knocks that box and the amount inside it off the game board. The amounts in the boxes are shown in the table at the top of the next page. 

After a few rounds, only the boxes below remain.

Find the following probabilities related to the next box selected:

P(the box $<$$€ 20$)

Write the answer up to $3$ decimal place.

The game Miljoenenjacht, which originally began in the Netherlands, is more widely known as Deal or No Deal. In the game, there are $26$ boxes, each with a different amount of money in it. At the beginning of the game, the player chooses one box which he/she hopes has the highest prize, $€ 5$ million. During the rest of the game, the player chooses boxes from those that remain. With each selection, the player knocks that box and the amount inside it off the game board. The amounts in the boxes are shown in the table at the top of the next page. 

After a few rounds, only the boxes below remain.

Find the following probabilities related to the next box selected:

P(the box $>€ 100000$)

Write the answer up to $3$ decimal place.

In the game of Risk, players set up armies on a map of the world that acts as the game board.

Players can add to their armies or wage war against armies in regions that are beside them. In these wars, each player rolls one or more six-sided dice, with each die representing a battle. With each battle, if the person initiating the war (the attacker) has a higher number, then he/she wins the battle. If the defender rolls a number that is equal to or greater than the attacker, then the defender wins the battle.

The number of dice rolled depends on the number of armies you have. When more than one die is rolled, whoever wins the most battles, wins the war. If each player wins the same number of battles, the defender wins the war.

Suppose each player rolls just one die. Find the probability that the defender wins the war if the attacker rolls a $3$. (Write the answer up to two decimal place).

In the game of Risk, players set up armies on a map of the world that acts as the game board.

Players can add to their armies or wage war against armies in regions that are beside them. In these wars, each player rolls one or more six-sided dice, with each die representing a battle. With each battle, if the person initiating the war (the attacker) has a higher number, then he/she wins the battle. If the defender rolls a number that is equal to or greater than the attacker, then the defender wins the battle.

The number of dice rolled depends on the number of armies you have. When more than one die is rolled, whoever wins the most battles, wins the war. If each player wins the same number of battles, the defender wins the war.

Suppose each player rolls just one die. Find the probability that the defender wins the war if the attacker rolls a $1$.

In the game of Risk, players set up armies on a map of the world that acts as the game board.

Players can add to their armies or wage war against armies in regions that are beside them. In these wars, each player rolls one or more six-sided dice, with each die representing a battle. With each battle, if the person initiating the war (the attacker) has a higher number, then he/she wins the battle. If the defender rolls a number that is equal to or greater than the attacker, then the defender wins the battle.

The number of dice rolled depends on the number of armies you have. When more than one die is rolled, whoever wins the most battles, wins the war. If each player wins the same number of battles, the defender wins the war.

Suppose each player rolls just one die. Find the probability that the defender wins the war if the attacker rolls a $5$. (Write the answer up to two decimal place)

In the game of Risk, players set up armies on a map of the world that acts as the game board.

Players can add to their armies or wage war against armies in the regions that are beside them. In these wars, each player rolls one or more six-sided dice, with each die representing a battle. With each battle, if the person initiating the war (the attacker) has higher number, then he/she wins the battle. If the defender rolls a number that is equal to or greater than the attacker, then the defender wins the battle.

The number of dice rolled depends on the number of armies you have. When more than one dice is rolled, whoever wins the most battles, wins the war. If each player wins the same number of battles, the defender wins the war.

Suppose each player rolls just one die. Find the probability that the defender wins if the attacker rolls a $6$ (rounded off to two decimal places).