There are 50 students in a class and the professor chooses 15 students at random. what is the probability that you or your friend joe are among the chosen students?

30% probability that Joe is among the chosen students.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the students are chosen is not important, so the combinations formula is used to solve this question.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

Desired outcomes:

Joe

14 remaining students, from the remaining 49. So

Total outcomes:

15 students, from a set of 50. So

Probability

30% probability that Joe is among the chosen students.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.