Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 18 Jul 2019, 06:38

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

When an unfair coin is tossed twice, the probability of getting one

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56251
When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 26 May 2015, 10:29
1
24
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

34% (02:06) correct 66% (01:44) wrong based on 179 sessions

HideShow timer Statistics


Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56251
Re: When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 01 Jun 2015, 03:09
1
5
Bunuel wrote:
When an unfair coin is tossed twice, the probability of getting one tails and one heads is 1/3. What is the probability of getting two heads and two tails if the coin is tossed 4 times?

A. 2/3
B. 1/3
C. 1/4
D. 1/6
E. 1/9


OFFICIAL SOLUTION:

Let the probability of heads be x and the probability of tails be 1-x.

So, we are given that P(one tails and one heads) = 2*x*(1-x) = 1/3.

P(two heads and two tails) = 4!/(2!2!)*x^2*(1-x)^2 = 6*(x*(1-x))^2. We are multiplying by 4!/(2!2!) because HHTT scenario can occur in several ways: HHTT, HTHT, THHT, ... (permutation of 4 letters HHTT where 2 T's and 2 H's are the same).

Since from 2*x*(1-x) = 1/3 it follows that x*(1-x) = 1/6, then 6*(x*(1-x))^2 = 6*(1/6)^2 = 1/6.

Answer: D.
_________________
Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 21 Feb 2012
Posts: 56
Re: When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 27 May 2015, 07:41
3
3
Hello all

My attempt:

Let \(x\) be the probability of getting a head. Therefore the probability of getting a tail will be \((1-x)\).
As per the given statement in the two tosses (successive events)
P(HT)+P(TH) = 1/3
\(x*(1-x) + (1-x)*x = 1/3\)
\(x*(1-x) = 1/6\)

For the new scenario we have the following combinations possible
\(P(4 tosses) = P(HHTT)+P(HTTH).....\)
In this case there will \(4!/(2!*2!)\) ways which is \(6\) ways.
Therefore
\(P(4 tosses) = 6*x^2*(1-x)^2\)
\(P(4 tosses) = 6*(1/6)^2\)
\(P(4 tosses) = 1/6\)

I will go with answer D.
_________________
Regards
J

Do consider a Kudos if you find the post useful
General Discussion
GMAT Tutor
avatar
G
Joined: 24 Jun 2008
Posts: 1726
Re: When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 26 May 2015, 11:47
Bunuel, can you check the answer choices here? I don't think the right answer is among the choices, whether I interpret order to matter or not.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56251
Re: When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 27 May 2015, 04:51
Intern
Intern
avatar
B
Joined: 11 Aug 2013
Posts: 8
Location: India
GRE 1: Q168 V150
GPA: 3.2
GMAT ToolKit User Reviews Badge
Re: When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 24 Sep 2018, 00:44
Bunuel wrote:
Bunuel wrote:
When an unfair coin is tossed twice, the probability of getting one tails and one heads is 1/3. What is the probability of getting two heads and two tails if the coin is tossed 4 times?

A. 2/3
B. 1/3
C. 1/4
D. 1/6
E. 1/9


OFFICIAL SOLUTION:

Let the probability of heads be x and the probability of tails be 1-x.

So, we are given that P(one tails and one heads) = 2*x*(1-x) = 1/3.

P(two heads and two tails) = 4!/(2!2!)*x^2*(1-x)^2 = 6*(x*(1-x))^2. We are multiplying by 4!/(2!2!) because HHTT scenario can occur in several ways: HHTT, HTHT, THHT, ... (permutation of 4 letters HHTT where 2 T's and 2 H's are the same).

Since from 2*x*(1-x) = 1/3 it follows that x*(1-x) = 1/6, then 6*(x*(1-x))^2 = 6*(1/6)^2 = 1/6.

Answer: D.



hi buneul


whats difference between fair and unfair coin??...

thanks
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56251
Re: When an unfair coin is tossed twice, the probability of getting one  [#permalink]

Show Tags

New post 24 Sep 2018, 01:10
sdgmat89 wrote:
Bunuel wrote:
Bunuel wrote:
When an unfair coin is tossed twice, the probability of getting one tails and one heads is 1/3. What is the probability of getting two heads and two tails if the coin is tossed 4 times?

A. 2/3
B. 1/3
C. 1/4
D. 1/6
E. 1/9


OFFICIAL SOLUTION:

Let the probability of heads be x and the probability of tails be 1-x.

So, we are given that P(one tails and one heads) = 2*x*(1-x) = 1/3.

P(two heads and two tails) = 4!/(2!2!)*x^2*(1-x)^2 = 6*(x*(1-x))^2. We are multiplying by 4!/(2!2!) because HHTT scenario can occur in several ways: HHTT, HTHT, THHT, ... (permutation of 4 letters HHTT where 2 T's and 2 H's are the same).

Since from 2*x*(1-x) = 1/3 it follows that x*(1-x) = 1/6, then 6*(x*(1-x))^2 = 6*(1/6)^2 = 1/6.

Answer: D.



hi buneul


whats difference between fair and unfair coin??...

thanks


In case of fair coin P(heads) = P(tails) = 1/2. If a coin is not fair, then the probabilities might be different.
_________________
GMAT Club Bot
Re: When an unfair coin is tossed twice, the probability of getting one   [#permalink] 24 Sep 2018, 01:10
Display posts from previous: Sort by

When an unfair coin is tossed twice, the probability of getting one

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne