Answer:
1/35
Step-by-step explanation:
1. We can think about this problem as the probability of 3 events happening.
The first event is the teacher choosing one student who does not play soccer. The second event is the teacher choosing another student who does not play soccer, given that the teacher already chose someone who does not play soccer , and so on.
2. The probability that the teacher will choose someone who does not play soccer is the number of students who do not play soccer divided by the total number of students: 3/7.
3. Once the teacher's chosen one student, there are only 6 left.
4. There's also one fewer student who does not play soccer, since the teacher isn't going to pick the same student twice.
5. So, the probability that the teacher picks a second student who also does not play soccer is 2/6.
6. The probability of the teacher picking two students who do not play soccer must then be 3/7*2/6.
7. We can continue using the same logic for the rest of the students the teacher picks.
8. So, the probability of the teacher picking 333 students such that none of them play soccer is:
3/7*2/6*1/5=6/210=1/35
The probability that none of the three of them play soccer is 1/35.
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have a total number of students = 7
In which the number of students who play soccer = 4
We know the probability
[tex]\rm = \frac{favorable \ outcome}{total \ outcome}[/tex]
Number of students who do not play soccer = 7-4⇒ 3
Total favorable outcome:
= [tex]_{3}^{}\textrm{C}_3[/tex]
= [tex]\frac{3!}{3!(3-3)!}[/tex]
= 1
Total outcomes:
= [tex]_{7}^{}\textrm{C}_3[/tex]
= [tex]\frac{7!}{3!(7-3)!}[/tex]
= 35
So the probability is
[tex]=\frac{1}{35}[/tex]
Thus, the probability that none of the three of them play soccer is 1/35.
Learn more about the probability here:
brainly.com/question/11234923
