Final answer:
The probability that a combination lock consists only of odd numbers can be calculated by determining the total number of possible combinations and the number of combinations with only odd numbers. The probability is approximately 0.004.
Step-by-step explanation:
To find the probability that the combination consists only of odd numbers on a combination lock with numbers from zero to nine, we need to determine the total number of possible combinations and the number of combinations that consist only of odd numbers.
Since there are ten numbers in total (from zero to nine) and a combination consists of numbers in a specific order with no repeats, we have a total of 10! (ten-factorial) combinations.
Out of these combinations, we can arrange odd numbers (1, 3, 5, 7, and 9) in 5! (five-factorial) ways.
Therefore, the probability that the combination consists only of odd numbers is 5! / 10! = 1/252, which is approximately 0.004.