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# What is the probability of getting at least 2 heads in a row

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What is the probability of getting at least 2 heads in a row [#permalink]  15 Apr 2012, 21:03
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What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

Intern
Joined: 17 Feb 2012
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Re: probability [#permalink]  15 Apr 2012, 21:56
1
KUDOS
If we don't read the question attentively, we will be very likely to make the wrong calculations. In my opinion:
1/2 X 1/2 X 1 (it doesen't matter) +
+
1/2 (the probability of not getting a head after the first flip) X 1/2 (the probability of getting a head) X 1/2( the probability of getting a head again)
=
1/4 + 1/8 = 3/8
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Senior Manager
Joined: 12 Mar 2012
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Re: probability [#permalink]  15 Apr 2012, 22:00
rovshan85 wrote:
what is the prob. of getting at least 2 heads in a row on three flips of a fair coin?

probability for HHT;

Total number of ways of arranging HHT keeping HH intact is 2!

probability = 2! * (1/2)^3

probability for HHH;

no of ways= 1

probability = (1/2)^3

hence required answer = 2! * (1/2)^3 + (1/2)^3
= 3* 1/8 = 3/8

Hope this helps...!!
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Re: What is the probability of getting at least 2 heads in a row [#permalink]  16 Apr 2012, 00:09
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Expert's post
rovshan85 wrote:
What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

The probability of at least 2 heads in a row on three flips is the sum of the probabilities of the following three cases: HHT, THH and HHH.

Now, each case has the probability of $$(\frac{1}{2})^3$$, so $$P=3*(\frac{1}{2})^3=\frac{3}{8}$$.

Hope it's clear.
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Re: What is the probability of getting at least 2 heads in a row [#permalink]  16 Apr 2012, 00:17
Banuel's explanation is again the simpliest and the steadiest against mistakes.
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Re: What is the probability of getting at least 2 heads in a row   [#permalink] 16 Apr 2012, 00:17
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