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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]

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Updated on: 09 Jul 2013, 13:48
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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

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.

Originally posted by josemnz83 on 09 Jul 2013, 13:44.
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]

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09 Jul 2013, 13:49
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3
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

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]

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

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04 Aug 2013, 14:44
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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]

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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 .
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On three consecutive flips of a coin, what is the probabilit  [#permalink]

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26 May 2019, 11:29
1
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

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.

TL;DR

HHH or TTT
Possible Cases: 2
Total Cases: 2^3 = 8
P = 2/8 = 1/4

or P = 1 * 1/2 * 1/2 = 1/4

Veritas Prep Official Solution

The trap answer here is 1/8 – you might look at this as a 1/2 probability on the first flip, then a 1/2 on the second, and a 1/2 on the third for a 1/8 probability, but remember – in this case the result of the first flip doesn’t have to be one or the other. Your job is just to match whatever the first result was on the next two. If the first was heads, then you need heads next (a 1/2 chance) and heads again (a 1/2 chance). And if it were tails, then you need tails (1/2) then tails (1/2). But because “any match will do” and you don’t care that it’s a specific match – the question doesn’t specify all heads or all tails, just “all of one of them” – your probability doubles because you’re not concerned about the result of the first event, you’re only concerned about matching whatever that result was.

General Tips

Credit: Veritas Prep

1) Check whether you need a *specific* pair/match or not.

2) If you don’t need a specific pair, but “any pair will do,” then the probability of the first result is 100% – something will happen.

3) If you need to guess, keep in mind that if it’s an unspecified pair/match, it’s almost certain that one of the trap answers will be a smaller number than the correct answer (in the above case, 1/8 is a trap and 1/4 is correct), so you can confidently rule out the smallest number and use number properties to try to eliminate another 1-2 answers.
On three consecutive flips of a coin, what is the probabilit   [#permalink] 26 May 2019, 11:29
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