Final answer:
To find the probability that a number formed by this program will be a multiple of 4, we consider the possible digit combinations. There are 324 possible combinations that form a multiple of 4 out of a total of 1296 possible combinations. Therefore, the probability is 0.25 or 25%.
Step-by-step explanation:
To find the probability that a number formed by this program will be a multiple of 4, we need to consider the possible digit combinations that can form a multiple of 4. A 4-digit number is divisible by 4 if the last two digits form a number divisible by 4. We have 6 possible digits (0, 1, 2, 3, 4, 5) for the last digit, and since the digit can be repeated, we have 6 choices for the second to last digit as well. This gives us a total of 6 x 6 = 36 possible combinations for the last two digits.
Next, we need to consider the first two digits of the 4-digit number. Since we are looking for even numbers, the first digit must be an even number, which is 0, 2, or 4. We have 3 choices for the first digit, and again, since the digit can be repeated, we have 3 choices for the second digit as well. This gives us a total of 3 x 3 = 9 possible combinations for the first two digits.
Finally, we multiply the number of possible combinations for the last two digits (36) by the number of possible combinations for the first two digits (9) to get the total number of 4-digit multiples of 4 that can be formed using the given digits. So the total number of favorable outcomes is 36 x 9 = 324.
The total number of possible outcomes is the total number of 4-digit numbers that can be formed using the given digits, which is 6 choices for each digit, so we have 6 x 6 x 6 x 6 = 64 = 1296.
Therefore, the probability of selecting a number that is a multiple of 4 is the number of favorable outcomes (324) divided by the total number of possible outcomes (1296):
Probability = 324 / 1296 = 0.25 or 25%