Solution:

To find the probability that a four-digit number comprising the digits 2, 5, 6, and 7 would be divisible by 4, we need to follow the steps given below:

Step 1: Find the total number of ways to form a four-digit number using the digits 2, 5, 6, and 7.

We can use the permutation formula to find the total number of ways to form a four-digit number using four distinct digits. Therefore, the total number of ways to form a four-digit number using the digits 2, 5, 6, and 7 is given by:

4P4 = 4! / (4-4)! = 24

Therefore, there are 24 possible four-digit numbers that can be formed using the digits 2, 5, 6, and 7.

Step 2: Find the number of four-digit numbers that are divisible by 4.

A number is divisible by 4 if and only if its last two digits are divisible by 4. Therefore, we need to consider only the last two digits of each four-digit number to determine if it is divisible by 4. We can use the following cases to find the number of four-digit numbers that are divisible by 4:

Case 1: The last two digits are 2 and 6.

In this case, the first two digits can be any of the remaining two digits. Therefore, the number of four-digit numbers that are divisible by 4 with the last two digits as 2 and 6 is:

2 x 1 x 1 = 2

Case 2: The last two digits are 6 and 2.

In this case, the first two digits can be any of the remaining two digits. Therefore, the number of four-digit numbers that are divisible by 4 with the last two digits as 6 and 2 is:

2 x 1 x 1 = 2

Case 3: The last two digits are 2 and 5.

In this case, the first two digits can be any of the remaining two digits. Therefore, the number of four-digit numbers that are divisible by 4 with the last two digits as 2 and 5 is:

2 x 1 x 1 = 2

Case 4: The last two digits are 6 and 5.

In this case, the first two digits can be any of the remaining two digits. Therefore, the number of four-digit numbers that are divisible by 4 with the last two digits as 6 and 5 is:

2 x 1 x 1 = 2

Therefore, the total number of four-digit numbers that are divisible by 4 is:

2 + 2 + 2 + 2 = 8

Step 3: Find the probability that a four-digit number comprising the digits 2, 5, 6, and 7 would be divisible by 4.

The probability of an event is the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability that a four-digit number comprising the digits 2, 5, 6, and 7 would be divisible by 4 is:

8 / 24 = 1 / 3

Therefore, the probability that a four-digit number comprising the digits 2, 5, 6, and 7 would be divisible by