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

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KAte and David each have $10. Together they flip a coin 5 [#permalink]

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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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Re: PS: Probability [#permalink]

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New post 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

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Re: PS: Probability [#permalink]

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New post 05 Aug 2008, 14:26
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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.

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Re: PS: Probability   [#permalink] 05 Aug 2008, 14:26
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KAte and David each have $10. Together they flip a coin 5

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