Dependent Probability

Question

In a class of 7, there are 4 students who play soccer..

If the teacher chooses 3 students, what is the probability that none of the three of them play soccer?

Answer 1

This is a Conditional Probability problem

If 4 out of 7 students play soccer

Then 3 out of 7 do not play soccer

The probability of choosing the first non-soccer player will be 3/7

That takes one away from those non-soccer players leaving 2 and it takes 1 away from the total students leaving 6 so the probability of choosing another non-soccer player will be 2/6

That takes one from the non-soccer players leaving 1 and takes a student away from the 6 leaving 5 so the last probability of choosing a non-soccer player is 1/5

Now you multiply the three probabilities together to get the final probability

(3/7)(2/6)(1/5)=6/210

Dividing 6 by 210 yields .0285714

Multiply by 100 to get a percent

2.9%