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22 Sep 2009, 13:36
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Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny$1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than$10 but less than $15? (A) 5/16 (B) 1/2 (C) 12/30 (D) 15/32 (E) 3/8 Source: Manhattan GMAT Archive (tough problems set).doc [Reveal] Spoiler: OA _________________ Please kudos if my post helps. Last edited by Bunuel on 17 Feb 2015, 11:34, edited 1 time in total. Renamed the topic, edited the question and added the OA. Kudos [?]: 293 [1], given: 18  Manhattan GMAT Discount Codes e-GMAT Discount Codes Magoosh Discount Codes Manager Joined: 22 Jul 2009 Posts: 191 Kudos [?]: 293 [1], given: 18 Re: Kate and Danny each have$10. Together, they flip a fair coin 5 times. [#permalink]

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22 Sep 2009, 13:40
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Decided to post this question as Manhattan's explanation was unnecessarily cumbersome.

Question asks for the probability of the coin landing tails up either 3 or 4 times = P(3t) + P(4t)

Binomial distribution formula: nCk p^k (1-p)^(n-k)

P(3t) = 5C3 (1/2)^3 (1/2)^2 = 10 (1/2)^5
P(4t) = 5C4 (1/2)^4 (1/2)^1 = 5 (1/2)^5

=> P(3t) + P(4t) = 15/32
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19 Oct 2011, 08:26
y arent we taking into account the probablility of 2 heads or 1

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Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] ### Show Tags 19 Oct 2011, 10:20 3 This post received KUDOS deep5586 wrote: y arent we taking into account the probablility of 2 heads or 1 For 2 & 1 heads Kate will end up with <$10 and we want her to win . Therefore, only possibilities are 3 or 4 heads.

I made an educated guess and it worked fine.

Ans- 'D'

MGMAT's anagram helped here as well.

HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10

Total acceptable cases = 15
Total cases = 32

P = 15/32
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31 Oct 2014, 01:56
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Bunuel wrote:

Tough and Tricky questions: Probability.

Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny$1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than$10 but less than $15? (A) 5/16 (B) 1/2 (C) 12/30 (D) 15/32 (E) 3/8 total number of possible outcomes when coin will be flipped 5 times= 2^5=32 now, for kate to have more than$10, she must have min. 3 favorable and max. 4 favorable draws in the 5 throws. (because if she wins in all the 5 draws, then she will have $15) kate will win, every time tails (T) appears on the coin. case 1) kate wins in 3 draws and losses in two. so we have 3 T's and 2H's(T,T,T,H,H), which can arrange themselves in 5!/(3!)(2!)=10 case 2) kate wins in 4 draws and losses in the 1 draw. so we have 4 T's and 1H (T,T,T,T,H), which can arrange themselves in 5!/4!=5 thus total no. of favorable ways=10+5=15 and thus required probability=15/32 Kudos [?]: 500 [4], given: 13 Intern Joined: 07 May 2015 Posts: 18 Kudos [?]: 6 [0], given: 9 Location: India Concentration: International Business, Finance GPA: 3.5 WE: Information Technology (Computer Software) Re: Kate and Danny each have$10. Together, they flip a fair coin 5 times. [#permalink]

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29 Jun 2015, 06:45
Solved it using Pascal's triangle method and able to got the answer in 30 sec. https://en.wikipedia.org/wiki/Pascal's_triangle

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Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] ### Show Tags 11 Dec 2017, 23:00 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Kudos [?]: 291 [0], given: 0 Re: Kate and Danny each have$10. Together, they flip a fair coin 5 times.   [#permalink] 11 Dec 2017, 23:00
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# Kate and Danny each have \$10. Together, they flip a fair coin 5 times.

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