A classroom contains 13 students. A student committee of 3 (president, vice-president, and treasurer) must be selected. Harry Potter will serve only as president and only if either of his friends Ron Weasley or Hermione Granger serve as vice president; otherwise he leaves the group. The others (including Ron and Hermione) have no such restrictions. What is the probability that Ron or Hermione become the president of this group

16.39%

Step-by-step explanation:

We have a total number of forms, which are as follows:

-Harry Potter will serve as President AND Ron will serve as Vice President AND anyone will serve as Treasurer:

p1 = 1P11 = 11! / (11-1) ! = 11

-Harry Potter will serve as President AND Hermione will serve as Vice President AND anyone who serves as Treasurer is:

p2 = 1P11 = 11! / (11-1) ! = 11

- Harry Potter will not serve as President means that no one except Harry Potter (12 remaining students) serve in three locations:

p3 = 12P3 = 12! / (12-3) ! = 1320

in total it would be:

11 + 11 + 1320 = 1342

Now the favorable cases are:

- Hermione becomes the president of this group, which means that anyone except Hermione and Harry Potter (11 remaining students) serve in the remaining two places:

p1 = 11P2 = 11! / (11-2) ! = 110

- Ron becoming the president of this group means that anyone except Ron and Harry Potter (remaining 8 students) serve in the remaining two places:

p2 = 11P2 = 11! / (11-2) ! = 110

adding it would be: 110 + 110 = 220

now then the final probability is the favorable cases among the totals:

220/1342 = 0.1639

Which means that the probability is 16.39%