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In order, Anna, Beth, and Carrie take turns flipping the

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Dan
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In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   Updated on: 17 Jun 2005, 03:15
In order, Anna, Beth, and Carrie take turns flipping the same fair coin. The first one to toss a head wins. What is the probability that Beth wins?

A. 1/4
B. 1/2
C. 1/3
D. 1/8
E. 2/7



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Originally posted by Dan on 16 Jun 2005, 23:30.
Last edited by Dan on 17 Jun 2005, 03:15, edited 1 time in total.
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christoph
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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   17 Jun 2005, 00:08
...its 1/4. i assume that beth wins but carrie has her chance as weil and she can toss head or tail. the question doesnt say that after one toss head the game will end...ok we can infer that it will end.but i learnt to stick very closely to what is being stated.
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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   17 Jun 2005, 00:34
since they all have equal chances of tossing H or T , then the prob of Bet winning seems 1/3
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Dan
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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   17 Jun 2005, 03:15
I added answer choices...
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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   17 Jun 2005, 04:43
Dan wrote:
In order, Anna, Beth, and Carrie take turns flipping the same fair coin. The first one to toss a head wins. What is the probability that Beth wins?

A. 1/4
B. 1/2
C. 1/3
D. 1/8
E. 2/7


prob(Beth wins) = 1/4 + 1/32 +...+ 1/4*(8^(n-1))
n goes to infinity

E, D, A are out since they are less than 1/4,

1/3? or 1/2 I have no idea how sum it up.
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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   17 Jun 2005, 05:09
For Beth to win, she has to be ths first one to toss heads, for every possible round (ad inifinitum)

1/4 + 1/8(1/4)+ (1/8)^2*1/4+....

This is an infinite geometric series, a+ar+ar^2...

The sum is a/1-r = 1/4/(1-1/8) = (1/4)/(7/8) = 2/7

Answer is E

Sparky, 2/7 > 1/4
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Dan
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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink] New post   17 Jun 2005, 06:36
well..what can I say?!

E is correct.



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Re: In order, Anna, Beth, and Carrie take turns flipping the [#permalink]
17 Jun 2005, 06:36
Moderator:
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