Question

Each time a class meets, the professor selects one student at random to explain the solution to a homework problem. There are 40 students in the class, and no one ever misses class. Luke is one of these students. What is the probability that Luke is selected both of the next two times that the class meets? (Hint: See Example 5.8 )

Short answer

The probability that Luke is selected both of the next two times that the class meets is \(\frac{1}{1600}\).

Step-by-step solution

Probability of Luke being selected in the first class

The class has 40 students and one student is chosen at random. So, the probability of Luke being chosen in one class is \(\frac{1}{40}\). This is because there is only 1 favorable outcome (Luke being chosen) out of 40 possible outcomes (any one of the 40 students being chosen).

Probability of Luke being selected in the second class

The scenario is the same for the second class. The probability of Luke being chosen again in the second class is also \(\frac{1}{40}\). This is because each class meeting is an independent event.

Probability Luke is selected in both classes

In order to find the probability that both independent events occur (Luke is selected in the first and second class), we simply multiply the probabilities from steps 1 and 2. So, the probability of Luke being selected both times is \(\frac{1}{40} * \frac{1}{40} = \frac{1}{1600}\).