GMAT Changed on April 16th - Read about the latest changes here

It is currently 24 May 2018, 07:08

Happening NOW:

INSEAD Rolling Out R1 Admission Decisions - Join CHAT Room2 to Get Latest Updates from Fellow Applicants


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

The probability is 1/2 that a certain coin will turn up head

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

Hide Tags

3 KUDOS received
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 26 Dec 2012, 06:53
3
This post received
KUDOS
23
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (00:43) correct 25% (00:44) wrong based on 1115 sessions

HideShow timer Statistics

The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16
Expert Post
9 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45360
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 26 Dec 2012, 06:59
9
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

7 KUDOS received
Manager
Manager
avatar
Joined: 02 Jan 2013
Posts: 57
GMAT 1: 750 Q51 V40
GPA: 3.2
WE: Consulting (Consulting)
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 04 Jan 2013, 18:27
7
This post received
KUDOS
1
This post was
BOOKMARKED
Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8
Intern
Intern
avatar
Joined: 27 Feb 2013
Posts: 4
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 16 Sep 2013, 12:09
caioguima wrote:
Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8


Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2.
According to my understanding, the prob of head is 1/2 and tail is 1/2.
So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3?
Kindly clarify.
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45360
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 16 Sep 2013, 12:17
Expert's post
10
This post was
BOOKMARKED
abhinaya wrote:
caioguima wrote:
Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8


Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2.
According to my understanding, the prob of head is 1/2 and tail is 1/2.
So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3?
Kindly clarify.


The point is that two heads and a tail can occur in three ways: HHT, HTH, THH. The probability of each case is 1/2*1/2*1/2.

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Manager
Manager
avatar
Joined: 21 Oct 2013
Posts: 189
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 20 Nov 2013, 05:41
1
This post received
KUDOS
Bunuel wrote:
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

Answer: D.


Bunuel, would you mind explaining how you find the power to which you have to raise? What if e.g. there is a bag with three marbles, blue, red and yellow. Now the question is e.g. "What is the probabilty to get a blue marble on at least 1 try if you try 4 times" (putting the marbles back all the time).

Would it be P(at least 1 blue marble) = 1 - P(none blue) = 1 - (2/3)^4 ??

Thanks for your explanation!
Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45360
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 20 Nov 2013, 05:51
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
unceldolan wrote:
Bunuel wrote:
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2)^3 = 7/8.

Answer: D.


Bunuel, would you mind explaining how you find the power to which you have to raise? What if e.g. there is a bag with three marbles, blue, red and yellow. Now the question is e.g. "What is the probabilty to get a blue marble on at least 1 try if you try 4 times" (putting the marbles back all the time).

Would it be P(at least 1 blue marble) = 1 - P(none blue) = 1 - (2/3)^4 ??

Thanks for your explanation!


Yes, that's correct, the power must be the number of tries.

For the original question: P(at last 1 tails) = 1 - P(all heads) = 1 - (1/2*1/2*1/2)= 1 - (1/2)^3 = 7/8.

For your example: P(at least 1 blue) = 1 - P(no blue) = 1- (2/3*2/3*2/3*2/3) = 1- (2/3)^4.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 21 Oct 2013
Posts: 189
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 20 Nov 2013, 06:35
ok great :) thank you!
1 KUDOS received
Intern
Intern
avatar
Joined: 25 Sep 2014
Posts: 7
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 28 Nov 2014, 11:48
1
This post received
KUDOS
First thing to do is to come up with the total number of possible outcomes:
The coin is tossed 3 times and there is an equal probability that the coin will turn up heads or tail on each toss (which means that each toss has only two possible outcomes)
_ _ _
2*2*2=2^3=8
Multiply the number of possible outcomes per toss to arrive at the total number of possible outcomes. If the Question would state that the coin is to be tossed four times, the total number of possible outcomes would simply imply another multiplication by 2 or 2^4 which is 16.

Next step is to find the number of scenarios that fulfill the condition the Question stem asks for. (At least one tail)
One can easily recognize that ALL scenarios BUT ONE will include at least one tail. I am talking about the scenario in which all three tosses result in heads.
--> HHH
So 7 out of 8 scenarios will include at least one tail. THH, HTH, HHT etc…
This is already your final answer. P(at least one tail) = 7/8
Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2442
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 07 Jul 2016, 10:16
1
This post received
KUDOS
Expert's post
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


In this problem, there are only two events that could occur for the 3 coin flips. Either the coin will land on tails zero times, or the coin will land on tails at least one time. (Remember that the phrase "at least one time" means "one or more."

Writing this in a probability statement yields:

P(landing on tails at least 1 time) + P(landing on tails zero times) = 1

Thus, we can say:

P(landing on tails at least 1 time) = 1 - P(landing on tails zero times)


Since we are tossing the coin 3 times, the outcome of zero tails in 3 tosses is the same as getting heads on all 3 tosses. We can calculate the probability of zero tails in 3 tosses as the probability of 3 heads in 3 tosses:

½ x ½ x ½ =1/8

Plugging this into our formula we have:

P(landing on tails at least 1 time) = 1 – 1/8

P(landing on tails at least 1 time) = 7/8

Answer is D.
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Intern
avatar
Joined: 21 Dec 2014
Posts: 7
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 14 Sep 2016, 01:44
Added info : Formula to solve similar questions

Let 'p' be the probability of getting a head and 'q' be the probability of getting a tail.
If 'n' coins are tossed or one coin is tossed 'n' times

Then \(^nC_r * p ^ r * q^{n-r}\) gives the probability of having r heads and n-r tails.
Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 530
The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 21 Feb 2018, 12:46
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16



let Tails be T and Heads be H so i need to toss ONE coin three times and the probability is as follows:

first attempt and probability :)
T
H
H

second attempt and probability :)
H
T
H

third attempt and probability :)
H
H
T

so what am i to do next ? :? after i tossed coin 3 times.... Why do you guys above me all mutiplying ? :)

we have one coin and it does not effect the next event so we need to add up, no ? :) :? hmm like this 1/2+1/2+1/2 =3/2 i thought this was answer...

When do i need to multiply or add in probabality ? Difference? :? :)

help niks18 :)
1 KUDOS received
BSchool Forum Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 2557
Location: India
GPA: 3.12
Premium Member CAT Tests
The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 21 Feb 2018, 12:57
1
This post received
KUDOS
Hey dave13

RULE: The probability of an event occurring can never be greater than 1.

So, whenever during the course of a problem you get a number
greater than 1 for a probability, be assured that you have made a mistake!

You need to multiply the probability when the events are to occur simultaneously, or consecutively. 
For example, when we get three heads,
the probability will be \(\frac{1}{2}*\frac{1}{2}*\frac{1}{2} = \frac{1}{8}\).

We need to add probabilities when the events are alternatives.
For example, when there are three cases that can happen.
You can get HHT, HTT, TTT(for the three coins problem) as possible options for at least one tail.
In order to get the final answer, you need to add the individual probabilities for all the three cases.

Coming back to the problem
An easy way to solve this question is to find the probability that no tail
turns up and reduce that from 1(the maximum probability that an event can occur)

The probability that a tail does not turn up when three coins are tossed is when we get a head
on each of these coin tosses, which is \(\frac{1}{2}*\frac{1}{2}*\frac{1}{2} = \frac{1}{8}\)

Probability (atleast one tail turns up) = 1-P(All heads) = \(1 - \frac{1}{8} = \frac{7}{8}\)(Option D)

Hope this helps you!
_________________

You've got what it takes, but it will take everything you've got

Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 530
The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 22 Feb 2018, 09:55
Bunuel wrote:
abhinaya wrote:
caioguima wrote:
Although Bunuel's approach is, also in my opinion, the best way to go for this sort of question, you could also arrive at the same answer by using the following line of thought:

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

H H T -> 3 * 1/2*1/2*1/2
H T T -> 3 * 1/2*1/2*1/2
T T T -> 1/2*1/2*1/2

P = 3/8 + 3/8 + 1/8 = 7/8


Hi,

Kindly explain why it is 3* 1/2 * 1/2 * 1/2.
According to my understanding, the prob of head is 1/2 and tail is 1/2.
So HHT just has to be 1/2 * 1/2 * 1/2.. Isn't it? why multiply by 3?
Kindly clarify.


The point is that two heads and a tail can occur in three ways: HHT, HTH, THH. The probability of each case is 1/2*1/2*1/2.




Hello Bunuel :-)

if two heads and a tail can occur in three ways: HHT, HTH, THH. The probability of each case is 3* 1/2*1/2*1/2.

then two tails and one heads can occure 3 times as well TTH, THT, HTT right ? 3 * 1/2*1/2*1/2.

and probabilty that all tails and zero heads TTT 1/2*1/2*1/2 (so here we dont need to multiply by 3 because there is only one combination)

am i thinking correctly ? thanks :)
Expert Post
Top Contributor
SVP
SVP
User avatar
P
Joined: 12 Sep 2015
Posts: 2466
Location: Canada
Re: The probability is 1/2 that a certain coin will turn up head [#permalink]

Show Tags

New post 23 Apr 2018, 13:29
Expert's post
Top Contributor
2
This post was
BOOKMARKED
Walkabout wrote:
The probability is 1/2 that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

(A) 1/8
(B) 1/2
(C) 3/4
(D) 7/8
(E) 15/16


When it comes to probability questions involving "at least," it's best to try using the complement.

That is, P(Event A happening) = 1 - P(Event A not happening)

So, here we get: P(getting at least 1 tails) = 1 - P(not getting at least 1 tails)
What does it mean to not get at least 1 tails? It means getting zero tails.
So, we can write: P(getting at least 1 tails) = 1 - P(getting zero tails)

Now let's calculate P(getting zero tails)
What needs to happen in order to get zero tails?
Well, we need heads on the first toss and heads on the second toss and heads on the third toss.
We can write P(getting zero tails) = P(heads on 1st AND heads on 2nd AND heads on 3rd)
This means that P(getting zero tails) = P(heads on 1st) x P(heads on 2nd) x P(heads on 3rd)
Which means P(getting zero tails) = (1/2)x(1/2)x(1/2)= 1/8

We're now ready to answer the question.
P(getting at least 1 tails) = 1 - P(not getting at least 1 tails)
= 1 - 1/8
= 7/8

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Re: The probability is 1/2 that a certain coin will turn up head   [#permalink] 23 Apr 2018, 13:29
Display posts from previous: Sort by

The probability is 1/2 that a certain coin will turn up head

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


cron

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

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

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®.