GATE | GATE-CS-2006 | Question 21

For each element in a set of size 2n, an unbiased coin is tossed. The 2n coin tosses are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is:
(A) (2nCn) / (4^n)

(B) (2nCn) / (2^n)
(C) 1 / (2nCn)
(D) 1/2


Answer: (A)

Explanation: The question is mainly about probability of n heads out of 2n coin tosses.
P = 2nCn∗((1/2)^n)∗((1/2)^n) = (2nCn) / (4^n)


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