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gmat club m05 Q17

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gmat club m05 Q17 [#permalink] New post 02 Apr 2010, 15:35
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Kate and David each have $10. Together they flip a coin 5 times. Every time the coin lands on heads, Kate gives David $1. Every time the coin lands on tails, David gives Kate $1. After the coin is flipped 5 times, what is the probability that Kate has more than $10 but less than $15?

A. 5/16
B. 15/32
C. 1/2
D 21/32
E 11/16


i can't understand their explanation :(
please help!
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Re: gmat club m05 Q17 [#permalink] New post 02 Apr 2010, 22:41
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If Kate has to win more than $10 but less than $15 she has to win at least 3 times and at most 4 times.
If she wins 1 or 2 times she will have less than $10 at the end whereas if she wins all the 5 times shell will have $15


The probability that Kate has more than $10 but less than $15
= probability of getting 3 tails in 5 tosses + probability of getting 4 tails in 5 tosses
= 5c3 * (1/2)^3* (1/2)^2 + 5c4 *(1/2)^4 * (1/2)
=15/32

Answer B
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Re: gmat club m05 Q17   [#permalink] 02 Apr 2010, 22:41
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