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# On three consecutive flips of a coin, what is the probabilit

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On three consecutive flips of a coin, what is the probabilit [#permalink]  09 Jul 2013, 13:44
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Question Stats:

70% (01:25) correct 30% (00:28) wrong based on 82 sessions
On three consecutive flips of a coin, what is the probability that all three produce the same result?

(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2

[Reveal] Spoiler:
I came up with (1/2)*(1/2)*(1/2) =1/8

However, the explanation states that the answer is 1/4.

On the Total GMAT book, I had the following question: If a fair coin is flipped three times, what is the probability that it will be heads all three times?

There the answer given is 1/8, which is what I came up with.

Am I missing something? I do not see any distinction between these two questions.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Jul 2013, 13:48, edited 1 time in total.
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Re: On three consecutive flips of a coin, what is the probabilit [#permalink]  09 Jul 2013, 13:49
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Expert's post
josemnz83 wrote:
On three consecutive flips of a coin, what is the probability that all three produce the same result?

(A) 1/16
(B) 1/8
(C) 1/4
(D) 3/8
(E) 1/2

[Reveal] Spoiler:
I came up with (1/2)*(1/2)*(1/2) =1/8

However, the explanation states that the answer is 1/4.

On the Total GMAT book, I had the following question: If a fair coin is flipped three times, what is the probability that it will be heads all three times?

There the answer given is 1/8, which is what I came up with.

Am I missing something? I do not see any distinction between these two questions.

TTT case --> P = (1/2)^3 = 1/8.
HHH case --> P = (1/2)^3 = 1/8.

P(TTT or HHH) = 1/8 + 1/8 = 1/4.

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Re: On three consecutive flips of a coin, what is the probabilit [#permalink]  04 Aug 2013, 14:37
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Re: On three consecutive flips of a coin, what is the probabilit [#permalink]  04 Aug 2013, 14:44
1
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fatimaba wrote:

probability for head = $$1/2$$
similarly probability for tails = $$1/2$$

case 1: all 3 times = head
in that case
probability $$= 1/2*1/2*1/2 = 1/8$$

case 2 : all tails then again probability will be $$1/8$$

so total probability will be $$1/8+1/8 = 1/4$$

hope it helps
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Re: On three consecutive flips of a coin, what is the probabilit [#permalink]  26 Nov 2014, 11:38
fatimaba wrote:

If they had to all three be heads, then the calculation would be 1/2 * 1/2 * 1/2 = 1/8

In addition to getting the chosen outcome if we get three heads, we know that also we have success if the the three are all tails. So right there you know that the probability is greater than the 1/8 for three heads.

How much greater?

Well we have success if they are all heads. The probability of that is 1/8.

We also have success if they are all tails. The probability of that is also 1/8.

So we add the two together for the total probability of success, which is 1/8 + 1/8 = 1/4, choose
[Reveal] Spoiler:
C
.
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Re: On three consecutive flips of a coin, what is the probabilit   [#permalink] 26 Nov 2014, 11:38
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