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What is the probability that Fatima gets fewer heads than tails if she flips 10 coins?

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What is the probability that Fatima gets fewer heads than tails if she flips 10 coins?

Dec 31, 2018

#1
+100814
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The  prob of gettint exactly 5 heads is 10C5 (0.5)^10 = 252/1024 = 63/256

So it seems logical that the prob of not getting 5 heads is 1-63/256 = 193/256

and hall of those would have fewer heads than tails

(193/256) /2 = 193/512

Dec 31, 2018
#2
+5088
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This is the correct answer which can be seen by evaluating

$$\sum \limits_{k=0}^4~\dbinom{10}{k}\left(\dfrac 1 2\right)^{10}= \dfrac{193}{512}$$

Rom  Dec 31, 2018