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# KAte and David each have \$10. Together they flip a coin 5

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VP
Joined: 21 Jul 2006
Posts: 1485
KAte and David each have \$10. Together they flip a coin 5 [#permalink]

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05 Aug 2008, 11:34
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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 tails \$1. After the coin is flipped 5 times, what is the probability that Gate has more than \$10 but less than \$15?

a) 5/16
b) 15/32
c) 1/2
d) 21/32
e) 11/16

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SVP
Joined: 07 Nov 2007
Posts: 1757
Location: New York

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05 Aug 2008, 11:52
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tarek99 wrote:
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 tails \$1. After the coin is flipped 5 times, what is the probability that Gate has more than \$10 but less than \$15?

a) 5/16
b) 15/32
c) 1/2
d) 21/32
e) 11/16

It should be probablity for Kate wins exactly 3 times or 4 times

If p = P(success) and q = P(failure) = 1 - p, and the Bernoulli trial is repeated n times, then the probability of r successes is

P (x=r) =NCr p^r q^(n-r)

P(x=3)+ P(x=4) = 5C3 (1/2)^3 (1/2)2 + 5C4 (1/2)^4 (1/2)
= 5C3+5C4 / 2^5 = (5+10)/32 = 15/32

WHAT IS OA?
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Director
Joined: 12 Jul 2008
Posts: 513
Schools: Wharton

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05 Aug 2008, 14:26
3
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tarek99 wrote:
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 tails \$1. After the coin is flipped 5 times, what is the probability that Gate has more than \$10 but less than \$15?

a) 5/16
b) 15/32
c) 1/2
d) 21/32
e) 11/16

B

In order for Kate to have more than \$10 and less than \$15, she needs to win 3 times or 4 times.

Total numbers of possibilities = 2^5 = 32

Total number of possibilities for Kate to win 3 times = 5 choose 3 = 10
Total number of possibilities for Kate to win 4 times = 5 choose 4 = 5

Probability = (10 + 5) / 32 = 15/32

This is also a problem that you can just write out all the combinations quickly, because there aren't that many.

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: PS: Probability   [#permalink] 05 Aug 2008, 14:26
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