For each element in a set of size 2n, an unbiased coin is tossed. The 2n coin tosses are independent. An element is chos...

Question

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 was a head. The probability that exactly n elements are chosen is:

A. C(2n,n) / 4^n
B. C(2n,n) / 2^n
C. 1 / C(2n,n)
D. 1 / 2^n

Accepted Answer

P(exactly n elements chosen) = C(2n,n) / 4^n. Answer: A. We have 2n independent Bernoulli(1/2) trials and want exactly n successes (heads). This is a binomial distribution with parameters N=2n and p=1/2. The probability of exactly n heads is C(2n,n) * (1/2)^n * (1/2)^n = C(2n,n) / 4^n.

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 was a head. The probability that exactly n elements are chosen is: A. C(2n,n) / 4^n B. C(2n,n) / 2^n C. 1 / C(2n,n) D. 1 / 2^n