Respuesta :
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]
The probability that exactly 2 out of a group of 4 randomly selected seventh-graders watched television last night is 0.223.
What is Probability?
The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that there are a total of 10 students, out of these 10 students, the student who is given a number between 0-7 are watching TV, therefore, 8 students are watching tv, while the student whom number 8 and 9 is allotted are not watching Tv, therefore, a total of two students are not watching tv.
The number of ways a group of four students can be selected from 10 students is,
[tex]10 \times 9 \times 8 \times 7 = 5040[/tex]
The number of ways in which a group of four students can be selected such that two are watching tv while two are not,
[tex]8 \times 7 \times 2 \times 1 = 112[/tex]
Now, the probability that exactly 2 out of a group of 4 randomly selected seventh-graders watched television last night can be written as,
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
[tex]\rm{Probability=\dfrac{112}{5040}= \dfrac{1}{45} = 0.0223[/tex]
hence, the probability that exactly 2 out of a group of 4 randomly selected seventh-graders watched television last night is 0.223.
Learn more about Probability:
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