A fair coin is tossed 5 times. What is the probability that : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 20 Feb 2017, 02:29
GMAT Club Tests

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A fair coin is tossed 5 times. What is the probability that

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

Hide Tags

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 22 Sep 2005
Posts: 276
Followers: 1

Kudos [?]: 194 [1] , given: 1

A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 24 May 2006, 22:30
1
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

58% (02:13) correct 42% (01:08) wrong based on 291 sessions

HideShow timer Statistics

A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?

A. 1/16
B. 5/16
C. 2/5
D. 13/16
E. 27/32
[Reveal] Spoiler: OA
SVP
SVP
avatar
Joined: 30 Mar 2006
Posts: 1737
Followers: 1

Kudos [?]: 79 [0], given: 0

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 24 May 2006, 22:44
5/16

Two heads can be in a toss of 5 times in 5C2 = 10 ways

Each way(number of times at least two heads will come) has a probability of 1/32.

Hence 10*1/32 = 5/16
1 KUDOS received
Director
Director
User avatar
Joined: 05 Feb 2006
Posts: 898
Followers: 3

Kudos [?]: 108 [1] , given: 0

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 24 May 2006, 22:45
1
This post received
KUDOS
It is B....

Total possible outcomes=2*2*2*2*2=32
Favourable outcomes=5C2=10

Probability=10/32=5/16....
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 11 May 2006
Posts: 258
Followers: 2

Kudos [?]: 23 [1] , given: 0

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 24 May 2006, 22:52
1
This post received
KUDOS
SimaQ wrote:
It is B....

Total possible outcomes=2*2*2*2*2=32
Favourable outcomes=5C2=10

Probability=10/32=5/16....


going by your logic - the favourable outcomes should be 5C2 + 5C3 +5C4 + 5C5 ( question says at least 2..right?)
= 10 + 10 + 5 + 1 =26

hence prob = 26/32 = 13/16
ie choice D
SVP
SVP
avatar
Joined: 30 Mar 2006
Posts: 1737
Followers: 1

Kudos [?]: 79 [0], given: 0

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 24 May 2006, 23:02
iced_tea wrote:
SimaQ wrote:
It is B....

Total possible outcomes=2*2*2*2*2=32
Favourable outcomes=5C2=10

Probability=10/32=5/16....


going by your logic - the favourable outcomes should be 5C2 + 5C3 +5C4 + 5C5 ( question says at least 2..right?)
= 10 + 10 + 5 + 1 =26

hence prob = 26/32 = 13/16
ie choice D


Yes.......
Calculated ofr only two heads.....

Favorable outcomes are 5C2+5C3 + 5C4+5C5
=> 10+10+5+1
=> 26
26/32 = 13/16

Hence D
Director
Director
User avatar
Joined: 05 Feb 2006
Posts: 898
Followers: 3

Kudos [?]: 108 [0], given: 0

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 24 May 2006, 23:45
Yep my bad..... missed the at least part.... must be more concentrated.
Senior Manager
Senior Manager
avatar
Joined: 22 Sep 2005
Posts: 276
Followers: 1

Kudos [?]: 194 [0], given: 1

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 25 May 2006, 12:17
I don't understand whu you sum up "10+10+5+1".

Can someone explain it?
Director
Director
User avatar
Joined: 05 Feb 2006
Posts: 898
Followers: 3

Kudos [?]: 108 [0], given: 0

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 25 May 2006, 22:31
netcaesar wrote:
I don't understand whu you sum up "10+10+5+1".

Can someone explain it?


We sum up the number of ways you can toss heads up 2 times, 3 times, 4 times and 5 times....
1 KUDOS received
Intern
Intern
avatar
Joined: 04 Dec 2013
Posts: 3
Followers: 0

Kudos [?]: 1 [1] , given: 10

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 06 Aug 2014, 19:43
1
This post received
KUDOS
Probability of all tails = 1/32
Probability of 4 tails = 5/32
------------------------------------------------------------------------------
Probability of all tails or 4 tails = 1/32 + 5/32 = 6/32 = (3/16)
------------------------------------------------------------------------------

Therefore probability of at least 2 heads = 1- Prob of all or 4 tails = 1- (3/16) = 13/16

Hence (D)
Intern
Intern
avatar
Joined: 12 Feb 2013
Posts: 10
Location: India
Concentration: Finance, Marketing
Followers: 1

Kudos [?]: 7 [0], given: 61

GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 07 Aug 2014, 09:22
1
This post was
BOOKMARKED
Fair coin is tossed 5 times . Hence total number of outcomes = 2^5 = 32.

Problem asks for probability of getting atleast heads twice. Hence if we calculate probability of getting Heads exactly once and probability of not getting Heads at all and subract it from the total probability of the event which is 1 (As total probability of certain event will be always 1) we can get the probability of getting atleast heads twice.

Probability of getting exactly one head and no heads= (Number of possible outcomes [ HTTTT , THTTT, TTHTT, TTTHT, TTTTH , TTTTT] = 6)/ (Total possible outcomes = 32)

=> 6/32 = 3/16

Hence probability of getting atleast heads twice = 1 - (3/16) = 13/16 => Choice [D]
Manager
Manager
User avatar
Status: folding sleeves up
Joined: 26 Apr 2013
Posts: 157
Location: India
Concentration: Finance, Strategy
GMAT 1: 530 Q39 V23
GMAT 2: 560 Q42 V26
GPA: 3.5
WE: Consulting (Computer Hardware)
Followers: 1

Kudos [?]: 87 [0], given: 39

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 17 Sep 2014, 06:14
netcaesar wrote:
A fair coin is tossed 5 times. What is the probability that it lands heads up at least twice?

A. 1/16
B. 5/16
C. 2/5
D. 13/16
E. 27/32


Sol:

2H3T, 3H2T, 4H1T, 5H calculating this will take longer than calculating 5T, 4T1H

lets calculate 5T, 4T1H

5T= 1/2^5 = 1/32
4T1H = (1/32) (5!/4!) = 5/32

5T+4T1H= 6/32 = 3/16

1- (5T+4T1H) = 1-3/16 = 13/16

(D)
Senior Manager
Senior Manager
User avatar
S
Joined: 26 Oct 2016
Posts: 271
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GPA: 4
WE: Education (Education)
Followers: 12

Kudos [?]: 24 [0], given: 699

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 05 Jan 2017, 06:12
1
This post was
BOOKMARKED
Here are the numbers to remember:

1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

The first row applies to 3 flip questions, the second to 4 flip questions and the third to 5 flip questions.
If we want at least 2 heads, we want 2 heads, 3 heads, 4 heads OR 5 heads. Pretty much whenever we see "OR" in probability, we add the individual probabilities.

Looking at the 5 flip row, we have 1 5 10 10 5 1. For 2H, 3H, 4H and 5H we add up the 3rd, 4th, 5th and 6th entries: 10+10+5+1=26.

Summing the whole row, we get 32.

So, the chance of getting at least 2 heads out of 5 flips is 26/32 = 13/16.
_________________

Thanks & Regards,
Anaira Mitch

Senior Manager
Senior Manager
User avatar
S
Joined: 26 Oct 2016
Posts: 271
Location: United States
Concentration: Marketing, International Business
Schools: HBS '19
GPA: 4
WE: Education (Education)
Followers: 12

Kudos [?]: 24 [0], given: 699

Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 05 Jan 2017, 06:12
Here are the numbers to remember:

1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

The first row applies to 3 flip questions, the second to 4 flip questions and the third to 5 flip questions.
If we want at least 2 heads, we want 2 heads, 3 heads, 4 heads OR 5 heads. Pretty much whenever we see "OR" in probability, we add the individual probabilities.

Looking at the 5 flip row, we have 1 5 10 10 5 1. For 2H, 3H, 4H and 5H we add up the 3rd, 4th, 5th and 6th entries: 10+10+5+1=26.

Summing the whole row, we get 32.

So, the chance of getting at least 2 heads out of 5 flips is 26/32 = 13/16.
_________________

Thanks & Regards,
Anaira Mitch

Intern
Intern
avatar
B
Joined: 09 Jun 2015
Posts: 7
Concentration: Entrepreneurship, Finance
Followers: 0

Kudos [?]: 0 [0], given: 9

GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 05 Jan 2017, 07:24
For all these kind of questions we can answer using this concept ( hope all of you might have studied during your school days):

Probability of 'r' success out of 'n' trials = = nCr (P)^r (Q)^n-r

P - probability of success
Q - probability of failure

According to this question :
We need to find probability of head >= 2 out of 5 trials.
P - probability of success = 1/2(probability of getting head out of a toss)
Q - probability of failure= 1/2(probability of getting tail out of a toss)

In mathematical form:
P(H>=2) = 1-P(H<2) = 1- (P( H=0) + P( H=1)).

P(H =0) = 5C0 (1/2)^0 (1/2)^5 = (1/2)^5---------- eqn 1

P(H =1) = 5C1(1/2)^1 (1/2)^4 = (5/2)^5---------- eqn 2

Finally,

1-P(H<2) = 1- (P( H=0) + P( H=1)) = 1 - ((1/2)^5)+(5/2)^5) = 1- (6 / 2^5) = 26/32= 13/16.


Final note, though this method looks lengthy, it will be applicable to all atleast,atmost and exactly equal to 'n' of questions in probability.

In GMAT, more than solving fast we have to keep our mind unstressed and fresh. So that we can be active for such a long exam.

Hope it helps [WINKING FACE]
Manager
Manager
User avatar
S
Joined: 02 Jan 2017
Posts: 65
Location: Canada
Followers: 0

Kudos [?]: 21 [0], given: 179

Reviews Badge
Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 18 Feb 2017, 08:15
Fair coin is tossed 5 times.total number of outcomes = 2^5 = 32

5C2 + 5C3 +5C4 + 5C5=10+10+5+1=26

26/32=13/16

Ans-D
Wharton Thread Master
avatar
B
Joined: 30 May 2015
Posts: 19
Followers: 1

Kudos [?]: 6 [0], given: 48

GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 18 Feb 2017, 13:37
prob = 1 -(heads at max once)
= 1 - (heads exactly zero times or heads exactly one times)

at max once means two cases:
case 1 : exactly zero heads
=> TTTTT
=> 1/32

case 2 : heads exactly once
=> HTTTT
=> (5!/4!)/32
=> 5/32

Now after putting the values
=> 1 -(heads at max once)
=> 1 - ((1/32) + (5/32))
=> 13/16
Manager
Manager
avatar
B
Joined: 04 Aug 2015
Posts: 65
Location: India
Concentration: Leadership, Technology
GMAT 1: 620 Q50 V25
GPA: 3.39
Followers: 0

Kudos [?]: 5 [0], given: 9

CAT Tests
Re: A fair coin is tossed 5 times. What is the probability that [#permalink]

Show Tags

New post 18 Feb 2017, 21:10
We will have the following cases: (2H, 3T); (3H, 2T); (4H, 1T); (5H)

Also, HHHTT is different from HTTHT. Therefore, for (2H, 3T) => (1/2)^5 * 5!/(3! * 2!) = 10/32

(3H, 2T) => 10/32 ; (4H, 1T) => 5/32 ; (5H) => 1/32

Total = 13/16. Option D.
Re: A fair coin is tossed 5 times. What is the probability that   [#permalink] 18 Feb 2017, 21:10
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Robert tossed a fair coin 3 times. What is the probability that the co Bunuel 4 27 Dec 2015, 08:04
22 Experts publish their posts in the topic A fair coin is tossed 6 times. What is the probability of getting no saikarthikreddy 14 23 Sep 2012, 02:34
25 Experts publish their posts in the topic A fair coin is tossed 4 times. What is the probability of gmihir 10 30 Apr 2012, 00:05
52 Experts publish their posts in the topic A fair coin is tossed 5 times. What is the probability of nusmavrik 23 20 Aug 2010, 04:39
40 Experts publish their posts in the topic A fair coin is tossed 10 times. What is the probability that LM 28 22 Dec 2007, 20:57
Display posts from previous: Sort by

A fair coin is tossed 5 times. What is the probability that

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.