A small community college in Ohio has four student organizations (A, B, C, and D). Organization A has 5 students, B has 8, C has 10, and D has 12. It is thought that new students have no preference for one of these organizations over the other. If seven new students are admitted to the college, what is the probability that one student will choose organization A, one will choose B, two will choose C, and three will choose D?
A) approximately .059
B) .200
C) approximately .243
D) Cannot be determined without additional information.

Question

Quizplus · Accepted Answer

The probability can be calculated using the multinomial distribution formula, which is suitable for this scenario where we have a specific number of outcomes (students joining each organization) out of a total number of trials (new students choosing organizations). The formula considers the total ways to distribute the new students among the organizations and the probability of each distribution, assuming each student has an equal chance of choosing any organization. Given the lack of preference among the organizations, the calculation is straightforward and does not require additional information about the organizations or the students.

A Small Community College in Ohio Has Four Student Organizations