3) Erik wants to form 4-digit integers using only the digits 1, 2, 3, and 4. He is allowed to
repeat digits. What is the probability that he forms a 4-digit integer where at least one digit
repeats? Express your answer as a common fraction.
I think 1/8 probability.
Can I see the work?
To find the probability that Erik forms a 4-digit integer where at least one digit repeats, we need to calculate the total number of valid outcomes and the number of desired outcomes.
Total number of valid outcomes:
Since Erik can repeat digits, he has 4 choices for each of the 4 digits, giving a total of 4 * 4 * 4 * 4 = 256 valid outcomes.
Number of desired outcomes:
We need to calculate the number of 4-digit integers where all digits are distinct and subtract it from the total number of valid outcomes.
Number of 4-digit integers with distinct digits:
For the first digit, Erik has 4 choices (1, 2, 3, or 4). After choosing the first digit, he has 3 choices left for the second digit, 2 choices for the third digit, and only 1 choice left for the last digit. So the number of 4-digit integers with distinct digits is 4 * 3 * 2 * 1 = 24.
Number of desired outcomes = Total number of valid outcomes - Number of 4-digit integers with distinct digits = 256 - 24 = 232.
Therefore, the probability that Erik forms a 4-digit integer where at least one digit repeats is 232/256 which simplifies to 29/32.