<p>A particular <img alt="$12$" height="12" src="https://latex.artofproblemsolving.com/e/d/f/edf074831eb5bc9e61d6d6e09f525a86e3068f6a.png" width="17" />-hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a <img alt="$1$" height="14" src="https://latex.artofproblemsolving.com/d/c/e/dce34f4dfb2406144304ad0d6106c5382ddd1446.png" width="11" />, it mistakenly displays a <img alt="$9$" height="12" src="https://latex.artofproblemsolving.com/b/f/2/bf2c9074b396e3af0dea52d792660eea1c77f10f.png" width="8" />. For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?</p>

Question No: 298

A particular $12$ -hour digital clock displays the hour and minute of a day. Unfortunately, whenever it is supposed to display a $1$ , it mistakenly displays a $9$ . For example, when it is 1:16 PM the clock incorrectly shows 9:96 PM. What fraction of the day will the clock show the correct time?

Editorial

Tags: Algebra Probability

Question Details