Final answer:
The probability that the first digit of a three-digit personal identification number is 6 is calculated by dividing the number of favorable outcomes (1) by the total number of possible outcomes (9), which is approximately 0.11111.
Step-by-step explanation:
The question asks for the probability that the first digit of a three-digit personal identification number, created using the digits 1-9 without repetition, is 6. To find this probability, we can use the basic principle that probability is equal to the number of favorable outcomes divided by the total number of possible outcomes.
In this case, the favorable outcome is the number 6 being the first digit. Since the digits 1-9 can all potentially be the first digit, there are 9 possible outcomes for the first digit. Therefore, the probability of the first digit being 6 is 1 out of 9 outcomes.
The calculation is 1/9, which is approximately 0.11111. Therefore, the correct answer is c) 0.11111.