GATE CSE
First time here? Checkout the FAQ!
x
+3 votes
571 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)   | 571 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 (9.1k 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?
+4 votes

Answer :Option A 

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

answered by Active (2k points)  
+3 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 (16.9k points)  
edited by


Top Users Jun 2017
  1. Bikram

    3686 Points

  2. Hemant Parihar

    1480 Points

  3. junaid ahmad

    1432 Points

  4. Arnab Bhadra

    1334 Points

  5. Niraj Singh 2

    1311 Points

  6. Rupendra Choudhary

    1194 Points

  7. rahul sharma 5

    1110 Points

  8. Arjun

    916 Points

  9. srestha

    898 Points

  10. Debashish Deka

    896 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 Jun 19 - 25
  1. Bikram

    1942 Points

  2. Niraj Singh 2

    1306 Points

  3. junaid ahmad

    502 Points

  4. sudsho

    410 Points

  5. just_bhavana

    368 Points


23,347 questions
30,050 answers
67,327 comments
28,372 users