SOLUTION: 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? b) 3 or 4 is

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Question 1125508: 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?
b) 3 or 4 is selected?
c) 3 is not selected?

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
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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  C%5B4%5D%5E2 = %284%2A3%29%2F2 = 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  3%2F6 = 1%2F2.

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  5%2F6.

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  3%2F6 = 1%2F2.

Solved.