by: bhanu29
6 mins
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1008:00 PM PDT
-09:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
Sep 0812:30 AM EDT
-01:30 AM EDT
Looking for your GMAT motivation to break through the score plateau? Pragati improved her score by massive 160 points with strategic guidance and hard-work! Find out how personalized mentorship and a strong mindset can turn GMAT struggles into success.
Sep 1001:00 AM EDT
-02:00 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Posts: 97
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:09) correct
34%
(02:26)
wrong
based on 546
sessions
History
Date
Time
Result
Not Attempted Yet
A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
A. 37/256
B. 56/256
C. 65/256
D. 70/256
E. 81/256
A. 37/256
B. 56/256
C. 65/256
D. 70/256
E. 81/256
aiming4mba
The probability that the coin will land tails side up more than five times equals to the sum of the probabilities that coin lands 6, 7 or 8 times tails side up.
\(P(t=6)=\frac{8!}{6!2!}*(\frac{1}{2})^8=\frac{28}{256}\), we are multiplying by \(\frac{8!}{6!2!}\) as the scenario tttttthh can occur in \(\frac{8!}{6!2!}=28\) # of ways (tttttthh, ttttthth, tttthtth, ... the # of permutations of 8 letters tttttthh out of which 6 t's and 2h's are identical);
\(P(t=7)=\frac{8!}{7!}*(\frac{1}{2})^8=\frac{8}{256}\), the same reason of multiplication by \(\frac{8!}{7!}=8\);
\(P(t=8)=(\frac{1}{2})^8=\frac{1}{256}\), no multiplication as the scenario tttttttt can occur only in one way;
\(P=\frac{28}{256}+\frac{8}{256}+\frac{1}{256}=\frac{37}{256}\).
Answer: A.
Hope it's clear.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
\(Prabability = \frac{Desired Outcomes}{Total Outcomes}\)
Total Outcomes = Coin has to be tossed 8 times and Each time it tossed will give any one of two results i.e. Head or tail. So Total Possible Outcomes = 2 X 2 X ......8 times = \(2^8\)
Desired Outcomes = We want Coin be landed with head up more than 5 times i.e. 6 times or 7 times or 8 times. It is same as choosing 6 places from 8 places OR choosing 7 places from 8 places OR choosing 8 places from 8 places = 8C6 + 8C7 + 8C8 = 28 + 8 + 1 = 37 (Remember AND=Multiplication, OR=Addition)
\(Prabability = \frac{37}{2^8} = \frac{37}{256}\)
Total Outcomes = Coin has to be tossed 8 times and Each time it tossed will give any one of two results i.e. Head or tail. So Total Possible Outcomes = 2 X 2 X ......8 times = \(2^8\)
Desired Outcomes = We want Coin be landed with head up more than 5 times i.e. 6 times or 7 times or 8 times. It is same as choosing 6 places from 8 places OR choosing 7 places from 8 places OR choosing 8 places from 8 places = 8C6 + 8C7 + 8C8 = 28 + 8 + 1 = 37 (Remember AND=Multiplication, OR=Addition)
\(Prabability = \frac{37}{2^8} = \frac{37}{256}\)
General Discussion
aiming4mba
More than 5 times tails = 6times +7times+8times = 8C6 + 8C7 + 8C8 = 37
- - - - - - - -
2 2 2 2 2 2 2 2
2^8 times total events and 37 events where tails side up .
So probability = 37/2^8 = 37/256 (Answer A)
Posts: 127
Bunuel
Hi Bunuel,
Could you please clarify why are we multiplying by (1/2)^8.
Thanks
mvictor
Board of Directors
Joined: 17 Jul 2014
Last visit: 14 Jul 2021
Posts: 2,116
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20 (WD)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE:General Management (Transportation)
Products:
8C6 * (1/2)^8 = 28 * (1/2)^8
8C7 * (1/2)^8 = 8 * (1/2)^8
8C8 * (1/2)^8 = 1 * (1/2)^8
28+8+1 = 37.
A
8C7 * (1/2)^8 = 8 * (1/2)^8
8C8 * (1/2)^8 = 1 * (1/2)^8
28+8+1 = 37.
A
Updated on: 29 Jul 2025, 06:36
Originally posted by BrushMyQuant on 16 Oct 2022, 10:07.
Last edited by BrushMyQuant on 29 Jul 2025, 06:36, edited 1 time in total.
Last edited by BrushMyQuant on 29 Jul 2025, 06:36, edited 1 time in total.
[quote="aiming4mba"]
Given that A fair coin with sides marked heads and tails is to be tossed eight times, and we need to find What is the probability that the coin will land tails side up more than five times?
Coin is tossed 8 times => Total number of cases = \(2^8\) = 256
P(More than 5 Tails) = P(Getting 6 Tails) + P(Getting 7 Tails) + P(Getting 8 Tails)
P(Getting 6 Tails)
Out of the 8 places lets pick the 6 places where Tail will come. This can be in 8C6 ways
= \(\frac{8!}{6!*(8-6)!}\) = \(\frac{8*7*6!}{6!*2!}\) = 28 ways
P(Tail) = P(head) = \(\frac{1}{2}\) in each case
=> P(Getting 6 Tails) = Number of ways * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) = 28 * \((\frac{1}{2})^8\) = \(\frac{28}{256}\)
P(Getting 7 Tails) = P(Getting 1 Head)
Out of the 8 places lets pick the 1 place where Head will come. This can be in 8C7 ways = 8 ways
=> P(Getting 7 Tails) = Number of ways * \((\frac{1}{2})^8\) = 8 * \((\frac{1}{2})^8\) = \(\frac{8}{256}\)
P(Getting 8 Tails)
There is only on way in which we can get 8 Tails
=> P(Getting 8 Tails) = 1 * \((\frac{1}{2})^8\) = \(\frac{1}{256}\)
P(More than 5 Tails) = P(Getting 6 Tails) + P(Getting 7 Tails) + P(Getting 8 Tails) = \(\frac{28}{256}\) + \(\frac{8}{256}\) + \(\frac{1}{256}\) = \(\frac{37}{256}\)
So, Answer will be A
Hope it helps!
Playlist on Solved Problems on Probability here
Watch the following video to MASTER Probability with Coin Toss Problems
_________________
Given that A fair coin with sides marked heads and tails is to be tossed eight times, and we need to find What is the probability that the coin will land tails side up more than five times?
Coin is tossed 8 times => Total number of cases = \(2^8\) = 256
P(More than 5 Tails) = P(Getting 6 Tails) + P(Getting 7 Tails) + P(Getting 8 Tails)
P(Getting 6 Tails)
Out of the 8 places lets pick the 6 places where Tail will come. This can be in 8C6 ways
= \(\frac{8!}{6!*(8-6)!}\) = \(\frac{8*7*6!}{6!*2!}\) = 28 ways
P(Tail) = P(head) = \(\frac{1}{2}\) in each case
=> P(Getting 6 Tails) = Number of ways * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) * \(\frac{1}{2}\) = 28 * \((\frac{1}{2})^8\) = \(\frac{28}{256}\)
P(Getting 7 Tails) = P(Getting 1 Head)
Out of the 8 places lets pick the 1 place where Head will come. This can be in 8C7 ways = 8 ways
=> P(Getting 7 Tails) = Number of ways * \((\frac{1}{2})^8\) = 8 * \((\frac{1}{2})^8\) = \(\frac{8}{256}\)
P(Getting 8 Tails)
There is only on way in which we can get 8 Tails
=> P(Getting 8 Tails) = 1 * \((\frac{1}{2})^8\) = \(\frac{1}{256}\)
P(More than 5 Tails) = P(Getting 6 Tails) + P(Getting 7 Tails) + P(Getting 8 Tails) = \(\frac{28}{256}\) + \(\frac{8}{256}\) + \(\frac{1}{256}\) = \(\frac{37}{256}\)
So, Answer will be A
Hope it helps!
Playlist on Solved Problems on Probability here
Watch the following video to MASTER Probability with Coin Toss Problems
_________________
How to Solve :
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
All Quant Topics Theory || Last Two Digits of Exponents Ending with 1, 2, 3, 4, 5, 6, 7, 8, 9 || Units' Digit Problems || Even and Odd || Divisibility Rules || Positive and Negative || Absolute Value Basics || Inequalities || Absolute Value + Inequality || Functions and Custom Characters || LCM & GCD || Remainders || Factors and Multiples || Arithmetic and Geometric Progression || Co-ordinate Geometry || Circles || Probability: Coin Toss || Work Rate || Statistics || Stem & Leaf Plot || Box And Whisker Plot
GMAT Club Topic Wise Problems
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
Moderator:
Announcements
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.