Question 400430
{{{((34C4)/(35C4))^30 = (31/35)^30 = 0.02623}}}, 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 {{{(34C4)/(35C4) = 31/35}}}. 
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 {{{((34C4)/(35C4))^30 = (31/35)^30}}}.