For the number to be divided by 25 it should have 25 as last two digits, so it means that we have fixed the last two digits of the number and the total number of doing this is 1.

Now talking about the first two digits and they can be any number from the given choices so we can fill that two spaces by two numbers and total number of ways of doing this are 2!.

So the total number which are formed by the given numbers and are also get divided by 25 are 2!= 2

Now total number which can be formed by given four digits are 4!= 24

Now probability of getting a number which is divisible by 25= (total number which get divided by 25/total number formed)

=> 2/24

=>1/12

To compare the probabilities of encountering 54 Sundays in a leap year and 53 Sundays in a non-leap year, we can analyze both situations:

I. The probability of encountering 54 Sundays in a leap year:
In a leap year, there are 366 days, and these 366 days can start on any day of the week. Therefore, there are 7 possibilities for the day on which the year starts. To have 54 Sundays, there must be 2 days that are not Sundays. Since there are 7 possibilities for the starting day, the number of ways to select 2 days out of the 7 days for non-Sundays is given by the combination formula C(7, 2).

II. The probability of encountering 53 Sundays in a non-leap year:
In a non-leap year, there are 365 days, and these 365 days can also start on any day of the week. There are 7 possibilities for the day on which the year starts. To have 53 Sundays, there must be 1 day that is not a Sunday. Therefore, the number of ways to select 1 day out of the 7 days for the non-Sunday is given by the combination formula C(7, 1).

Let’s compare these probabilities:

I. Probability of 54 Sundays in a leap year = C(7, 2)
II. Probability of 53 Sundays in a non-leap year = C(7, 1)

We can calculate these values:

I. C(7, 2) = 21
II. C(7, 1) = 7

Now, let’s compare I and II:

I (21) > II (7)

So, the answer is Type 1, which means that the probability of encountering 54 Sundays in a leap year is greater than the probability of encountering 53 Sundays in a non-leap year.

To calculate the probability that the red ball selected is the smallest red ball, let’s consider the total number of ways to select a red ball and the number of ways to select the smallest red ball.

Total number of red balls = 6

Number of ways to select the smallest red ball = 1 (there is only one smallest red ball)

Probability = (Number of ways to select the smallest red ball) / (Total number of red balls)

Probability = 1/6

So, the correct answer is 1/6.

To make a profit of one rupee per throw of the die in the long run, the player should pay an amount equal to the expected value of the die roll. The expected value of a fair six-sided die roll is calculated by taking the average of all possible outcomes.

The expected value = (1/6) * (1) + (1/6) * (2) + (1/6) * (3) + (1/6) * (4) + (1/6) * (5) + (1/6) * (6)
Expected value = (1/6) * (1 + 2 + 3 + 4 + 5 + 6)
Expected value = (21/6)
Expected value = 7/2 = Rs. 3.50

So, the player should pay Rs. 3.50 to make a profit of one rupee per throw of the die in the long run.