Question

If you glance at a 12-hour digital clock at random, there is a 50-percent chance, exactly, that the time will contain which digit?

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) 8
10) 9

Answer 1

The digit '1' likely has the highest probability of appearing on a 12-hour digital clock display because it appears in both the hour and minute segments frequently. To be exactly certain, a probability analysis is required accounting for the occurrence of each digit in the 12-hour cycle.

Step-by-step explanation:

The question being asked is a probability question regarding the occurrence of a digit on a 12-hour digital clock. A 12-hour digital clock displays time in the format hh:mm, where hh can range from 01 to 12 and mm can range from 00 to 59. To find the digit that has a 50-percent chance of being in the time displayed, we can analyze the frequency of each digit in a 12-hour cycle.

Let's start with the digit '1'. It appears in the hours from 10 to 12 and as the first digit of minutes from 10 to 19, making for a high frequency of appearance. Therefore, it is likely that the digit '1' has a high probability of occurring. In contrast, the digit '2' occurs less frequently as it only appears in the hours from 02 to 12 for one hour each and as the second digit for minutes 20-29. Other digits, such as '0', '3', '4', '5', and so on, will also appear with varying frequencies within each hour.

In conclusion, the digit '1' seems to have the highest probability of occurring at a glance because it appears so frequently both as part of the hour and as part of the minute, making it a strong candidate for the digit that would be seen 50-percent of the time. However, to claim exact certainty, one would need to conduct a thorough probability analysis, factoring in the exact number of occurrences of each digit within the 12-hour cycle.