Question 1142643: An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade. If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A?
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20064)   (Show Source):
You can put this solution on YOUR website!
It's 1 minus the probability that NO student gets an A.
The probability that a student does not get an A is 100%-5% = 95% = 0.95
The probability that 50 students do not get an A is 0.9550 = 0.0769449753.
Therefore the probability that at least one will get an A is
1 - 0.0769449753 = 0.9230550247 or about 92.3% of the time.
Edwin
Answer by ikleyn(52893)  (Show Source):
You can put this solution on YOUR website! .
An experienced teacher writes an exam so that, on average, about 5% of students will earn an A grade.
If she has 50 students in her class and their performance is independent, what is the probability that at least one student gets an A?
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I am writing my post with the only one goal: to explain (and to make it clear the fact) that Edwin solved, actually,
different problem than is written in the post.
The problem solved by Edwin is THIS:
The class contains 50 students. On exam, the probability that every single student will earn an A grade is 5%.
What is the probability that at least one student gets an A ?
My formulation is CRYSTALLY clear, and it is an example (A STANDARD, actually) on how such problems MUST BE FORMULATED.
The original formulation in the post is very blurred,
and I do not think that it can, in general, be solved as it is formulated.
Edwin made it absolutely correct, when he changed the original formulation;
but he did it without acknowledgment, which, in my view, is not right.
I hope (and I am almost sure) that Edwin understands it well,
but I am writing these words for the future generations of students who will read this post (if they do . . . ).
As it was formulated in the post originally, is totally different problem.
/\/\/\/\/\/\/\/
At this forum, I am observing last days A FLOW of problems VERY poorly and badly formulated.
My impression is that they are / were created by person having zero knowledge on WHAT IS a Math problem
and how it should be formulated.
My hypothesis is that some former English teacher on the phone, without an experience in Math,
receives formulation from the outside and dispatches them to the forum and back, making small business . . .
It is the only way on how I can explain this flow of false Math problems arriving to the forum.
If it is so, then I INSISTENTLY recommend to the managers of this project to REPLACE this person URGENTLY,
since he (or she) is not able to perform his (or her) functions properly.
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