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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]

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15 Apr 2012, 22:03
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What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

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15 Apr 2012, 22:56
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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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15 Apr 2012, 23:00
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]

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16 Apr 2012, 01:09
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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]

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16 Apr 2012, 01:17
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]

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12 Dec 2015, 03:43
Hello from the GMAT Club BumpBot!

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Re: What is the probability of getting at least 2 heads in a row [#permalink]

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06 Apr 2017, 12:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the probability of getting at least 2 heads in a row [#permalink]

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14 Apr 2017, 05:46
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rovshan85 wrote:
What is the probability of getting at least 2 heads in a row on three flips of a fair coin?

We can assume the first two flips are heads (H) and the last flip is tails (T). Thus:

P(H-H-T) = 1/2 x 1/2 x 1/2 = ⅛

The only other way to get two heads in a row would be flipping heads on the second and third flips.

P(T-H-H) = 1/2 x 1/2 x 1/2 = ⅛

Thus, the total probability of getting two heads in a row when we flip a coin three times is 1/8 + 1/8 = 2/8.

Next, we need to determine the probability of getting heads on all three flips.

P(H-H-H) = 1/2 x 1/2 x 1/2 = 1/8.

Thus, the probability of getting at least two heads in a row is 2/8 + 1/8 = 3/8.
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Re: What is the probability of getting at least 2 heads in a row   [#permalink] 14 Apr 2017, 05:46
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