8,075 views
36 votes
36 votes

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

  1. $\frac{^{2n}\mathrm{C}_n}{4^n}$
  2. $\frac{^{2n}\mathrm{C}_n}{2^n}$
  3. $\frac{1}{^{2n}\mathrm{C}_n}$
  4. $\frac{1}{2}$

7 Answers

2 votes
2 votes

We can also put small values for n and eliminate options.

0 votes
0 votes
sample space : 2 * 2 * 2 … *2    ( 2n) times i.e. $2^{2n}$ which is $4^{n}$

favourable outcomes : chosing exactly n heads out of 2n tosses which is $^{2n}C_{n}$

 

(option A)

$\frac{^{2n}C_{n}}{4^{n}}$
0 votes
0 votes

 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)
Answer: (A)

Answer:

Related questions

41 votes
41 votes
5 answers
6
72 votes
72 votes
8 answers
7
Ishrat Jahan asked Nov 3, 2014
30,243 views
An unbiased coin is tossed repeatedly until the outcome of two successive tosses is the same. Assuming that the trials are independent, the expected number of tosses is$3...