+0  
 
+1
33
2
avatar

The display of a 24-hour digital clock shows hours and minutes in the format XX:XX. For what fraction of a day is at least one 2 displayed on this clock?

 

Can someone please help me solve this.

Guest Feb 13, 2018
Sort: 

2+0 Answers

 #1
avatar+333 
+1

The probability that the last digit is NOT a 1 is 9/10. The probability that the penultimate digit (i.e. first digit of the minutes portion) is NOT a 2 is 5/6. The probability that the hour portion does not contain a 2 is 8/12, for 12-hour displays, or 12/24, for 24-hour displays. (The teaser needs to state whether it is a 12- or 24-hour display.) Thus, for 12-hour displays, the probability of at least one 2 is: 1 - (9/10 * 5/6 * 8/12) = 1/2 and for 24-hour displays, is: 1 - (9/10 * 5/6 * 1/2) = 3/8

lynx7  Feb 13, 2018
 #2
avatar+82916 
+1

Answered better by lynx above  !!!!

 

cool cool cool

CPhill  Feb 13, 2018
edited by CPhill  Feb 13, 2018

14 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details