Electric Clock Probability Calculation

To calculate the probability that the second hand of an electric clock, stopped by a power failure, is between the 7 and the 11, we need to analyze the total time and the specific range of the clock face.

An electric clock has a full round of 60 seconds, representing 100% of the time. The space between the 7 and the 11 on the clock face represents 20 seconds, which is 1/3 of the total time (as 20 is 1/3rd of 60).

Therefore, by considering equal probability across all 60 seconds, the probability of the second hand stopping between the 7 and the 11 is calculated as 1/3 or 0.3333, often represented as 33.33%.

This calculation is based on a simplified assumption and does not take into account factors like the width of the hand or other variables related to how a clock operates.

It is an interesting scenario to consider, as the second hand of a clock is a continuous variable, making the probability of it being stopped at any specific point technically zero. However, by defining a specific range (such as between the 7 and the 11) and assuming a random stopping point within that range, we can estimate a probability.

If we assume that the second hand is equally likely to stop at any point between the 7 and the 11, and the second hand completes a full rotation in 60 seconds, the probability is determined by the ratio of the angle subtended by the range between the 7 and the 11 to the total angle of the clock.