Last visit was: 05 Sep 2026, 07:45 It is currently 05 Sep 2026, 07:45
Home
Messages
Tests
Schools
Events
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
avatar
araspai
avatar
Joined: 27 Jul 2003
Last visit: 24 Jan 2004
Posts: 92
Own Kudos:
209
Location: Singapore
Posts: 92
Kudos: 209
A and B alternately toss a coin. The first one to turn up a 09 Oct 2003, 21:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A and B alternately toss a coin. The first one to turn up a head wins. if no more than five tosses each are allowed for a single game., find the probability that the person who tosses first will win the game. What are the odds against A's losing if she goes first?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
Praetorian
User avatar
Joined: 15 Aug 2003
Last visit: 27 Dec 2017
Posts: 2,867
Own Kudos:
1,741
Given Kudos: 781
Posts: 2,867
Kudos: 1,741
A and B alternately toss a coin. The first one to turn up a 10 Oct 2003, 00:57
Kudos
Add Kudos
Bookmarks
Bookmark this Post
araspai
A and B alternately toss a coin. The first one to turn up a head wins. if no more than five tosses each are allowed for a single game., find the probability that the person who tosses first will win the game. What are the odds against A's losing if she goes first?
Show more

Quote:
find the probability that the person who tosses first will win the game.
Show more

1/2

Quote:
What are the odds against A's losing if she goes first
Show more


prob of A losing is 1/2

odds? dont know
User avatar
AkamaiBrah
User avatar
GMAT Instructor
Joined: 07 Jul 2003
Last visit: 24 Jun 2009
Posts: 390
Own Kudos:
538
Location: New York NY 10024
Concentration: Finance
Schools:Haas, MFE; Anderson, MBA; USC, MSEE
Posts: 390
Kudos: 538
A and B alternately toss a coin. The first one to turn up a 16 Oct 2003, 00:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
araspai
ans 21/32, 21:11
Show more


Would you be kind enough to please explain the answer so we can all understand how it was arrived at?
User avatar
am1974
User avatar
Joined: 11 Mar 2003
Last visit: 11 Nov 2003
Posts: 27
Own Kudos:
1
Location: Chicago
Posts: 27
Kudos: 1
A and B alternately toss a coin. The first one to turn up a 18 Oct 2003, 17:23
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here is what I think how this problem should be worked upon.

The first question asks to find the probability that the person who tosses first will win the game. Any one of A or B can tosse first. Let us say that A tosses first. So basically we need to find the probability that A will win.

The game can follow in the following possible ways:

A B A B A B A B A B

H....end of game A wins
T H ......end of game B wins
T T H ..... end of game A wins
T T T H.....end of game B wins
T T T T H .....end of game A wins
T T T T T H .....end of game B wins
T T T T T T H ....end of game A wins
T T T T T T T H ....end of game B wins
T T T T T T T T H ....end of game A wins
T T T T T T T T T H ....end of game B wins
T T T T T T T T T T ....NOBODY wins ...tie

First question:

ONLY 1, 3, 5, and 7th options above are applicable for the first question. Because these are the only options where A wins.

Probability for the firts option = 1/2
Probability for the 3rd option = 1/8 and so on

The probability that A wins (the one who tossed first) = 1/2 + 1/8 + 1/32 + 1/128 + 1/512 = 341/512.

I know this answer is different from what araspai has mentioned. But it is approximately ~ 21.3/32. May be it is correct answer.

SECOND QUESTION

Here the condition is given that A tosses first. The above configuration will work for this condition. So we do not need to create a new configiration.

Here I really have concern about the answer araspai has given (probability > 1?)

IMHO, the "odds against A's loosing" = Probability of A wining OR probability of occuring a tie

we already found the probability of A wining = 341/512

based on the above configuration of all the possible game options,

the probability of occuring a TIE = 1/1024 (The last option)

Hence, the "odds against A's loosing" = 341/512 + 1/1024 = 643/1024.

araspai,

can you tell us if these answers seem reasonable?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!