The probability that the sum of the number on tickets is 25/256 and the correct option is A.
To determine the probability of the sum of the numbers on the tickets being 23, we'll analyze the possible outcomes of drawing five tickets from the bag.
The total number of ways to draw five tickets from the bag is 4^5 = 1024.
To find the number of ways to get a sum of 23, we can consider the problem as a combination of 4 numbers from the set {0, 1, 10, 11} that add up to 23.
We can use generating functions to solve this problem. Let's define generating functions for the individual numbers:
f_0(x) = 1 + x
f_1(x) = 1 + x
f_{10}(x) = 1 + x^2
f_{11}(x) = 1 + x^2
The generating function for the sum of the numbers is the product of the individual generating functions:
F(x) = f_0(x) * f_1(x) * f_{10}(x) * f_{11}(x)
Expanding the product, we get:
F(x) = (1 + x) * (1 + x) * (1 + x^2) * (1 + x^2)
= 1 + 4x + 6x^2 + 4x^3 + x^4 + 4x^5 + 6x^6 + 4x^7 + x^8
The coefficient of x^23 in this expansion represents the number of ways to get a sum of 23. Using polynomial long division or a computer algebra system, we can find that the coefficient of x^23 is 24.
Therefore, the number of ways to get a sum of 23 is 24.
The probability of getting a sum of 23 is the number of successful outcomes divided by the total number of possible outcomes:
Probability = 24/1024 = 3/128 = 25/256.
So the correct option is A.