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.
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