Probability of 0-6 Students in Class of 20 - Help!

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In summary: If there were 100 students then the chance of 8 students being in that category would be 100% no?"No, if the probability of a student being in a certain category is any number less than 1.00, no matter how many students you have in a class, there is always some probability that NONE of the students are in that category and some probability that ALL are.
  • #1
dranger35
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I haven't done a probability problem in a long time. Thank you.

Assume that 8 % of the students fall in some particular
category. We have 20 students in our class. What is the
probability that we have 0, 1, 2, 3, 4, 5, or 6 of those students in
our class?
 
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  • #2
Binomial distribution. If the probability of a "success" in one "trial" is p, then the probability of a "failure" is 1-p. The probability of exactly i "successes" in n "trials" (and so n-i "failures") is [tex]_nC_i p^i q^{n-i}[/tex] where [tex]_nC_i[/tex] is the "binomial coefficient" [tex]\frac{n!}{i!(n-i)!}[/tex]).

The probability that anyone student is in that category is 0.08 so the probability a student is NOT in that category is 0.92. The probability exactly i students out of 20 are in that category is [tex]\frac{20!}{i!(20-i)!}i^{0.08}(20-i)^{0.92}[/tex].

Calculate that for i= 0, 1, 2, 3, 4, 5, 6 and add.

(Sorry, I left out the "[ tex ]" originally)
 
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  • #3
Ok

Thanks a lot I needed it
 
  • #4
Wait

What did you mean by frac in the beginning of the equation and tex in tha last part.?
 
  • #5
dranger35 said:
What did you mean by frac in the beginning of the equation and tex in tha last part.?
I think it's just a typo. The correction would be [tex]\frac{20!}{i!(20-i)!}i^0.08(20-i)^0.92[/tex]
 
  • #6
I don't know anything about probability but I would like to and I just had a thought.

If there were 100 students then the chance of 8 students being in that category would be 100% no? However, the chances of 7 students or 9 would being in that category would be lass than 100%. So their is a maximum and and it seems you could graph the probabilities verses the number of students and it would be parabola?
 
  • #7
I think that's the idea of the bell curve.
 
  • #8
dranger35 said:
What did you mean by frac in the beginning of the equation and tex in tha last part.?

I accidently left out the beginning "tex" tag. I edited to fix that.

honestrosewater: It's good to know I'm not the only one who messes up latex! (Or did you do that intentionally to make me feel better?)

You need { } in "i^{0.08}"

slug:"If there were 100 students then the chance of 8 students being in that category would be 100% no?"

No, if the probability of a student being in a certain category is any number less than 1.00, no matter how many students you have in a class, there is always some probability that NONE of the students are in that category and some probability that ALL are. You are, however, correct that the probability is highest at the "expected value" which, for a binomial distribution is np. In the orginal problem that is (20)(0.08)= 1.6 (round to 2) and if n= 100, 8.
But it's not a parabola (for one thing probability is never negative!)- it is, as philosophking said, a bell-shaped curve: basically given by [tex]e^{-x^2}[/tex].
 
  • #9
HallsofIvy said:
honestrosewater: It's good to know I'm not the only one who messes up latex! (Or did you do that intentionally to make me feel better?)

You need { } in "i^{0.08}"
Actually, I just copy-pasted what you had written and added the beginning [ tex ]. Oddly enough I did wonder if that was correct- but you had just written [tex]_nC_i p^i q^{n-i}[/tex] correctly so figured you knew to include the braces. Funny. I do mess up though- that's why I preview before posting. :biggrin:
 

FAQ: Probability of 0-6 Students in Class of 20 - Help!

What is the probability of having exactly 0 students in a class of 20?

The probability of having exactly 0 students in a class of 20 is extremely low, as it would mean that no one enrolled or attended the class. This probability would depend on the specific circumstances and factors that may lead to an empty classroom.

What is the probability of having exactly 6 students in a class of 20?

The probability of having exactly 6 students in a class of 20 can vary depending on the specific factors and circumstances. However, assuming a random selection process, the probability can be calculated using the binomial distribution formula, which would give a result of approximately 0.013 or 1.3%.

What is the probability of having less than 6 students in a class of 20?

The probability of having less than 6 students in a class of 20 would depend on the specific factors and circumstances. However, assuming a random selection process, the probability can be calculated using the binomial distribution formula, which would give a result of approximately 0.043 or 4.3%.

What is the probability of having more than 6 students in a class of 20?

The probability of having more than 6 students in a class of 20 would depend on the specific factors and circumstances. However, assuming a random selection process, the probability can be calculated using the binomial distribution formula, which would give a result of approximately 0.957 or 95.7%.

What factors can affect the probability of having 0-6 students in a class of 20?

There are many factors that can affect the probability of having 0-6 students in a class of 20. Some examples include enrollment trends, class scheduling, class subject or topic, location of the class, and availability of alternative options for students. Additionally, external factors such as weather or unexpected events can also impact the probability.

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