Question 1192631
**a. Probability of a visit taking at least 15 minutes**

* **Uniform Distribution:** In a uniform distribution, the probability density function is constant within the given interval.
* **Calculate the total interval:** 
    * Total interval = 25 minutes - 10 minutes = 15 minutes
* **Calculate the probability density:**
    * Probability density (f(x)) = 1 / (total interval) = 1 / 15 
* **Calculate the probability of a visit taking at least 15 minutes:**
    * This is the probability of the visit taking between 15 minutes and 25 minutes.
    * Length of this interval: 25 minutes - 15 minutes = 10 minutes
    * Probability = (length of interval) * (probability density) = 10 minutes * (1/15) = 2/3 

**Therefore, the probability that a randomly selected cable repair visit will take at least 15 minutes is 2/3 or approximately 0.667.**

**b. Probability of a visit taking over 20 minutes given it takes over 15 minutes**

* **Conditional Probability:** We are given that the visit takes over 15 minutes. This becomes our new "total interval."
* **New total interval:** 25 minutes - 15 minutes = 10 minutes
* **Length of the interval where the visit takes over 20 minutes:** 25 minutes - 20 minutes = 5 minutes
* **Probability:** 5 minutes / 10 minutes = 1/2

**Therefore, the probability that a cable repair visit will take over 20 minutes given that it takes over 15 minutes is 1/2 or 0.5.**