An electric clock is stopped by a power failure. What is the probability that the second hand is stopped between the 2 and the 5?

The probability is [tex]$\square$[/tex] (Type a simplified fraction.)



Answer :

Certainly! Let's walk through the detailed solution step-by-step:

1. Understand the problem: We want to find the probability that the second hand of a clock stops between 0 and 5 seconds.

2. Identify the total possible outcomes: The second hand of a clock can stop at any position between 0 and 60 seconds. This means there are 60 possible outcomes, each representing one second.

3. Determine the successful outcomes: The second hand must stop between 0 and 5 seconds to be considered a successful outcome. This includes the following seconds: 0, 1, 2, 3, and 4. Therefore, there are 5 successful outcomes.

4. Calculate the probability: The probability of an event is given by the ratio of the number of successful outcomes to the total number of possible outcomes.

[tex]\[ \text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{60} \][/tex]

5. Simplify the fraction:

[tex]\[ \frac{5}{60} = \frac{1}{12} \][/tex]

So, the probability that the second hand is stopped between 0 and 5 seconds is:

[tex]\[ \boxed{\frac{1}{12}} \][/tex]