Official Solution:
An electronic clock displays time in hours and minutes. For instance, 08:15 represents a quarter past eight. If someone looks at the clock at a random time between 6:00 (inclusive) and 9:00 (exclusive) what is the probability that he will see the digit 8?
A. \(\frac{1}{5}\)
B. \(\frac{1}{3}\)
C. \(\frac{2}{5}\)
D. \(\frac{4}{9}\)
E. \(\frac{1}{2}\)
The period between 6:00 (inclusive) and 9:00 (exclusive) spans 180 minutes. To find the probability of seeing the digit 8 during this time, we will analyze each hour separately.
1. Between 6:00 and 6:59, there are 6 instances when the digit 8 appears: 06:08, 06:18, 06:28, 06:38, 06:48, and 06:58.
2. Between 7:00 and 7:59, there are also 6 instances when the digit 8 appears: 07:08, 07:18, 07:28, 07:38, 07:48, and 07:58.
3. Between 8:00 and 8:59, the digit 8 appears in every minute (e.g., 08:01, 08:02, 08:03, etc.). So the number of minutes with the digit 8 is 60.
In total, there are 6 + 6 + 60 = 72 minutes with the digit 8 between 6:00 (inclusive) and 9:00 (exclusive). Therefore, the desired probability is given by \(\frac{72}{180} = \frac{2}{5}\).
Answer: C