SOLUTION: Suppose there are 35 students in a class and 30 lectures in 1 semester. If 4 students are randomly picked in a class to answer questions, what is the probability that one student

Question 400430: Suppose there are 35 students in a class and 30 lectures in 1 semester. If 4 students are randomly picked in a class to answer questions, what is the probability that one student is never called during the semester?
I would say almost 0% but I don't know where to begin.
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose there are 35 students in a class and 30 lectures in 1 semester. If 4 students are randomly picked in a class to answer questions, what is the probability that one student is never called during the semester?
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Binomial Problem with n = 4*30 = 120 and p(not called) = 34/35
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P(x = 0) = (34/35)^120 = 0.031
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Cheers,
Stan H.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
, to 5 decimal places.
To explain the answer, consider excluding student A, e.g., from the class of 35. Then there are 34C4 possible ways of selecting groups of 4 students from the remaining 34 students.
The total number of groups of 4 students coming from the entire class of 35 is 35C4 (regardless whether person A is included or not.)
Hence in a particular lecture, the probability of person A not being included in the group of 4 students is .
Since the event of student A not being called in any of the 30 lectures is identically and independently copied for all 30 lectures, the probability is .
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