kutkut wrote:What is the probability that, twelve seconds from a randomly selected starting time, a certain digital clock will display a number of seconds x such that x < 10 ?
(A) 19/60
(B) 3/10
(C) 1/5
(D) 11/60
(E) 1/6

The key thing to realize is that:
The probabilty that 0 seconds from a starting time, the clock will display a number of seconds x such that x < 10 is equal to,
The probabilty that 5 seconds from a starting time, the clock will display a number of seconds x such that x < 10 is equal to,
The probabilty that 10 seconds from a starting time, the clock will display a number of seconds x such that x < 10

Therefore we eliminate the phrase "twelve seconds from a randomly selected starting time"

The re-phrased qustion is: What is the probability that a clock will display a number of seconds x such that x < 10 ?

x<10 means x could be 0 to 9 which are 10 choices
We know the total number of seconds the clock can display is 60 [0sec - 59sec]

therefore probability = 10/60 = 1/6
ans = e

The part about the 12 seconds from not is irrelevant. So you have 10 number 0 - 9, out of a possible 60. 10/60 = 1/6