NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 20:06 It is currently 25 Apr 2024, 20:06
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A coin that is tossed will land heads or tails, and each outcome has

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619041 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
A coin that is tossed will land heads or tails, and each outcome has [#permalink] New post   29 Oct 2018, 01:06
2
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

77% (00:40) correct 23% (00:38) wrong based on 132 sessions
Hide Show timer Statistics
A coin that is tossed will land heads or tails, and each outcome has equal probability. What is the probability that the coin will land heads at least once on two tosses?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 3/4
ShowHide Answer
Official Answer
E
User avatar
G
Salsanousi
Senior Manager
Senior Manager
Joined: 19 Oct 2013
Posts: 412
Own Kudos [?]: 306 [0]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Send PM
GMAT ToolKit User
Re: A coin that is tossed will land heads or tails, and each outcome has [#permalink] New post   29 Oct 2018, 05:15
The probability of at least one heads in two flips = 1 - probability of no heads

Probability of no heads in both flips = 1/2 * 1/2 (both are tail)

so 1 - 1/4 = 3/4

Or we can do it in the longer way

One heads, one tails = 1/2 * 1/2 = 1/4
One tail and one heads = 1/2 * 1/2 = 1/4
Two heads = 1/2 * 1/2 = 1/4

Add them we get 3/4

Answer choice E
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5960
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
A coin that is tossed will land heads or tails, and each outcome has [#permalink] New post   29 Oct 2018, 05:49
1
Kudos
Expert Reply
Bunuel wrote:
A coin that is tossed will land heads or tails, and each outcome has equal probability. What is the probability that the coin will land heads at least once on two tosses?

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


Total outcomes when a coin is tossed twice = 2*2 = 4

METHOD 1:
Case 1: Exactly 1 Head outcomes will be HT or TH i.e. 2 outcomes
Case 2: Exactly 2 Head outcomes will be HH i.e. 1 outcome

Favourable Outcomes = 3

Probability = 3/4

METHOD 2:

Unfavourable case is when None of the toss results in a Head i.e. Both Tails i.e. TT i.e. 1 outcome

Unfavourable Probability = 1/4

Favourable Probability = 1- Unfavourable probability = 1- (1/4) = 3/4

Answer: Option E
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16841 [0]
Given Kudos: 165
Send PM
Re: A coin that is tossed will land heads or tails, and each outcome has [#permalink] New post   30 Oct 2018, 03:24
Expert Reply

Solution


Given:
    • Each outcome of a fair coin has equal probability

To find:
    • Probability of atleast one heads

Approach and Working:
    • Total number of outcomes = 2 * 2 = 4, which are {HH, HT, TH, TT}
      o Among these 3 outcomes have atleast one heads, {HH, TH, HT}

    • Therefore, the probability of atleast one heads = \(\frac{3}{4}\)

Hence, the correct answer is Option E

Answer: E

User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1777
Own Kudos [?]: 2094 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: A coin that is tossed will land heads or tails, and each outcome has [#permalink] New post   16 Oct 2022, 11:17
Expert Reply
Top Contributor
Given that A fair coin is tossed twice, and we need to find What is the probability that the coin will land heads at least once on two tosses?

P(At least one Head) = 1 - P(0 head) = 1 - P(TT)
= 1 - \(\frac{1}{2}\) * \(\frac{1}{2}\) (As P(T) in each toss = \(\frac{1}{2}\) )
= 1 - \(\frac{1}{4}\) = \(\frac{3}{4}\)

So, Answer will be E
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

GMAT Club Bot
gmatclubot
Re: A coin that is tossed will land heads or tails, and each outcome has [#permalink]
16 Oct 2022, 11:17
Moderators:
Bunuel
Math Expert
92915 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions