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The names of four students are placed in a small box and two will be selected. Let 1, 2, 3 and 4 denote the students. What is the probability that:
a) 3 is selected ?
In all, there are = = 6 groups of 2 students, that can be formed of 4 students.
Of these 6 groups, exactly 3 groups contain "3". They are (3,1), (3,2), and (3,4).
Thus the probability under the question a) is = .
b) 3 or 4 is selected ?
There is ONLY ONE group of two students, which contain NEITHER "3" NOR "4".
This group is (1,2).
The rest 5 of 6 groups necessary / inevitably contain EITHER "3" OR "4".
Thus the probability under the question b) is .
c) 3 is not selected ?
As we saw in the n. a), there are 3 groups of two students that contain "3".
Hence, of the total possible 6 groups three contain "3", while 3 other do not.
Thus the probability under the question c) is = .
Solved.