math II probability problem..again

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1

<p>I've been coming across pretty hard (for me) probability problems lately, so I'll just keep on posting them here...</p>

<p>This one is from Sparknotes Math II test</p>

<p>A two sided coin is flipped four times. Given that the coin landed heads up more than twice, what is the probability that it landed heads up all four times?</p>

<p>(a) 1/16
(b) 1/6
(c) 1/5
(d)1/2
(e)1/4</p>

<p>The answer is (c).</p>

<p>I think that if it's already given that the coin lands heads up either 3 or 4 times, then the probability of either one should be 1/2.</p>

<p>Can anyone please explain this problem to me?</p>

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<p>There are 16 different outcomes possible to 4 consecutive flips.
You can enumerate them :
TTTT
TTTH
TTHT
TTHH
etc… until HHHH</p>

<p>There are only 5 occurences where H appears at least 3 times (more than twice)
these are:
THHH
HTHH
HHTH
HHHT
HHHH
so, 5 occurences in total, while all four heads appears only once
the probability that all four flips produce H is therefore 1/5 given that heads appear more than twice</p>