Question

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. What is the probability that none of the members chosen for the team have any competition experience?
A) 0.1538
B) 0.2538
C) 0.3538
D) 0.4538

Answer 1

Answer:

A) 0.1538

Step-by-step explanation:

4 members are going to be chosen:

M1 - M2 - M3 - M4

We have to find the probability that for each member, one without experience is chosen. There is no replacents.

Initially, we have 15 students, of which 10 have none experience. So the probability that M1 is chosen as a student with no experience is $\frac{10}{15}$.

Then, there are 14 students, of which 9 have no experience. So the probability that M2 is chosen as a student with no experience is $\frac{9}{14}$.

For the third member, there are 13 students, of which 8 have no experience. So the probability that M3 is chosen as a student with no experience is $\frac{8}{13}$.

For the last member, there are 12 students, of which 7 have no experience. So the probability that M4 is chosen as a student with no experience is $\frac{7}{12}$.

What is the probability that none of the members chosen for the team have any competition experience?

This is

$P = \frac{10}{15}*\frac{9}{14}*\frac{8}{13}*\frac{7}{12} = 0.1538$

The correct answer is:

A) 0.1538