Question

For what fraction of a day will a 12-hour digital clock that shows only the hours and minutes display at least one 5 or 6

Answer 1

Answer: 4/9

Explanation:

Find out combinations without 5 or 6.

Minutes with 5 or 6: 05,06,15,16,25,26,35,36,45,46,50–59. It 10+10=20 minutes per hour. And 40 minutes without 5 or 6.

Hours with 5 or 6: 5 and 6. Without 5 and 6 is 0,1,2,3,4,7,8,9,10,11 (10 hours).

Total time without 5 and 6 is 10*40minutes=400 minutes.

Time with 5 or 6 is 12*60–400=320 minutes.

Fraction of a day: 320/(12*60)=4/9=0.44444