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kate and david

by gmatrix » Tue Aug 10, 2010 9:16 am
source-gmat club test

Kate and David each have $ 10.Together they flip a coin 5 times.Every times 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.
[spoiler]Ans-15/32[/spoiler]
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by kmittal82 » Tue Aug 10, 2010 10:02 am
Here is the key:
Probability of finding exactly k number of outcomes in n number of flips = nCk/2^n

e.g., exactly 3 heads in 5 coin flips = 5c3/2^5

The only way Kate can have more than $10 and less than $15 is either of the two scenarios:

1) 3 tails and 2 heads:

probabiliy = 5c3/2^5 = 10/32

2) 4 tails and 1 head:

proability = 5c4/2^5 = 5/32

Total probability = 15/32
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