Q:

The numbers 0–7 represent students who watched television last night, and the numbers 8 and 9 represent students who did not. Based on the simulated data, what is the probability that exactly 2 out of a group of 4 randomly selected seventh-graders watched television last night?

Accepted Solution

A:
Answer:[tex]\frac{1}{45}[/tex]Step-by-step explanation:We have total of 10 students - 8 watching TV and 2 not watching.We need to randomly select 4 students, from which half watched and half did not watch TV,So if we have 4 slots for students, and for each one we randomly choose a student. For first 2 slots lets assume we want to get those who watched TV, then probabilities for those are:[1] [tex]\frac{students who watched TV}{all students}  = \frac{2}{10}[/tex] for second one, we do the same, but removing already choosen student in [1]:[2] [tex] \frac{1}{9}[/tex]  now we have 2 slots left and 8 student left, out of which all have watched TV. So we have 100% that we will randomly choose 2 more studets, who watched TV.So total probability is:[tex]\frac{2}{10}*\frac{1}{9}  *1*1 = \frac{2}{90}  = \frac{1}{45}[/tex]