Question

A lazy high school senior types up application and envelopes to and different colleges, but puts the applications randomly into the envelopes. What is the expected number of applications that went to the right college?

Answer 1

To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. The expected number of applications that went to the right college is 1.

Step-by-step explanation:

To calculate the expected number of applications that went to the right college, we need to consider the probability of each application being placed correctly. Since the applications are placed randomly, each application has an equal chance of going to the right college. Let's say there are n applications and n colleges.

The probability of a specific application going to the right college is 1/n. Therefore, the expected number of applications that went to the right college can be calculated as:

Expected number = Total number of applications * Probability of an application going to the right college

Expected number = n * (1/n)

Expected number = 1

The expected number of applications that went to the right college is 1. This means that, on average, one application will go to the right college.