GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
475 views

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. $\frac{1}{2}$
asked in Probability by Loyal (4k points)   | 475 views

3 Answers

+9 votes
Best answer

answer - A

ways of getting n heads out of 2n tries = 2nCn

probability of getting exactly n heads and n tails = (1/2n)(1/2n)

number of ways = 2nCn/4n

answered by Boss (9k points)  
selected by
what if we do as below:
no. of ways to get n heads = 2nCn
no. of total outcome = 2n
therefore, probability of getting exactly n heads out of 2n tosses = 2nCn /2n

what does it calculate?
How is it saying n heads out of 2n?
+2 votes

Required Probability=$\frac{No. of Favourable Ways }{Total no. of Ways}$

No. of favourable ways= 2nC (bcoz select exactly n heads out of 2n tosses )

Total no. of ways= 2n tosses and each have 2 possibilities either H or T so total=$2^{2n}$=$4^n$ possibilities

So Ans is $\frac{\binom{2n}{n} }{4^{n}}$  which fits option A.

answered by Veteran (16.2k points)  
edited by
+1 vote

Answer :Option A 

Here is the link for theory- http://stattrek.com/probability-distributions/binomial.aspx
 

answered by Active (1.7k points)  
Members at the site
Top Users Feb 2017
  1. Arjun

    4680 Points

  2. Bikram

    4004 Points

  3. Habibkhan

    3738 Points

  4. Aboveallplayer

    2966 Points

  5. sriv_shubham

    2278 Points

  6. Smriti012

    2212 Points

  7. Arnabi

    1814 Points

  8. Debashish Deka

    1788 Points

  9. sh!va

    1444 Points

  10. mcjoshi

    1444 Points

Monthly Topper: Rs. 500 gift card

20,788 questions
25,938 answers
59,533 comments
21,926 users