SOLUTION: What is the probability of obtaining exactly eight heads in nine flips of a coin, given that at least one is a head? Can I get a little bit of help this evening? This one is t

Question 493384: What is the probability of obtaining exactly eight heads in nine flips of a coin, given that at least one is a head?

Can I get a little bit of help this evening? This one is too hard to try and solve on my own.Thanks very much!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
What is the probability of obtaining exactly eight heads in nine flips of a coin, given that at least one is a head?
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P(8 H in 9 flips | >= 1 H)
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= P(8 H in 9 flips AND >= 1 H)/P(at least one H)
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Ans = P(8 H in 9 flips) / P(at least one H)
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P(8 H in 9 flips) = 9C8(1/2)^9 = 9/2^9
P(at least one H) = 1 - P(no H) = 1 - (1/2)^9
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Therefore: Ans = [9/2^9]/(1 - (1/2)^9)
= [9/2^9]/[(2^9-1)/2^9]
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= 9/[2^9-1]
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Cheers,
Stan H.
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