GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
491 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)   | 491 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 (9.2k 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 (16.3k 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)  


Top Users Mar 2017
  1. rude

    4768 Points

  2. sh!va

    3054 Points

  3. Rahul Jain25

    2920 Points

  4. Kapil

    2734 Points

  5. Debashish Deka

    2592 Points

  6. 2018

    1544 Points

  7. Vignesh Sekar

    1422 Points

  8. Akriti sood

    1342 Points

  9. Bikram

    1312 Points

  10. Sanjay Sharma

    1126 Points

Monthly Topper: Rs. 500 gift card

21,508 questions
26,832 answers
61,091 comments
23,146 users