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Probability - Kate & Danny

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by cypherskull » Sat Aug 25, 2012 7:56 am
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


I'm invariably making the same mistake in probability questions over and over. Yet, I'm never really sure where I'm going wrong. This is how I approached the problem and got an answer which is nowhere in the options :cry:

Kate wins all 5 = Kate ends with $15
Kate wins 4 & Danny wins 1 = Kate ends with $13
Kate wins 3 & Danny wins 2 = Kate ends with $11
Kate wins 2 & Danny wins 3 = Kate ends with $9
Kate wins 1 & Danny wins 4 = Kate ends with $7
Kate wins 0 & Danny wins 5 = Kate ends with $5

Reqd probability = Desired results (in bold face)/All possibilities = 2/6 = 1/3

Obviously, I'm wrong! Experts please help me with the required concepts here!!
Regards,
Sunit

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by GaneshMalkar » Sat Aug 25, 2012 10:39 am
cypherskull wrote: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


I'm invariably making the same mistake in probability questions over and over. Yet, I'm never really sure where I'm going wrong. This is how I approached the problem and got an answer which is nowhere in the options :cry:

Kate wins all 5 = Kate ends with $15
Kate wins 4 & Danny wins 1 = Kate ends with $13
Kate wins 3 & Danny wins 2 = Kate ends with $11
Kate wins 2 & Danny wins 3 = Kate ends with $9
Kate wins 1 & Danny wins 4 = Kate ends with $7
Kate wins 0 & Danny wins 5 = Kate ends with $5

Reqd probability = Desired results (in bold face)/All possibilities = 2/6 = 1/3

Obviously, I'm wrong! Experts please help me with the required concepts here!!

The order of the head or tail matters as it is stick to money :) Its a permutation problem!!!

Total number of possibilities = 2^5

Now to get kate more than 10 and less than 15, kate has to win 4 or 3 times....

Probability of getting 4 wins = P(4) = 5C4 / 2^5 = 5/32
Probability of getting 3 wins = P(3) = 5C3 / 2^5 = 10/32

Total probability = 15/32
If you cant explain it simply you dont understand it well enough!!!
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by GMATGuruNY » Sat Aug 25, 2012 6:18 pm
Check my posts here:

https://www.beatthegmat.com/probability-t72568.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
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