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A coin with heads on one side and tails on the other has a 1/2 probabi

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A coin with heads on one side and tails on the other has a 1/2 probabi  [#permalink]

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New post 03 Jan 2019, 09:18
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A coin with heads on one side and tails on the other has a 1/2 probability of landing on heads. If the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be heads? Outcomes are distinct if they do not contain exactly the same results in exactly the same order.

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16

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Re: A coin with heads on one side and tails on the other has a 1/2 probabi  [#permalink]

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New post 03 Jan 2019, 09:47
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Bunuel wrote:
A coin with heads on one side and tails on the other has a 1/2 probability of landing on heads. If the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be heads? Outcomes are distinct if they do not contain exactly the same results in exactly the same order.

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16


Take the task of listing possible outcomes and break it into stages.

Stage 1: Select an outcome for the 1st flip
The flip can be heads or tails.
So, we can complete stage 1 in 2 ways

Stage 2: Select an outcome for the 2nd flip
The flip can be heads or tails.
So, we can complete stage 2 in 2 ways

Stage 3: Select an outcome for the 3rd flip
We can complete this stage in 2 ways

Stage 4: Select an outcome for the 4th flip
We can complete this stage in 2 ways

Stage 5: Select an outcome for the LAST flip
This flip MUST be heads.
So, we can complete this stage in 1 way


By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus list possible outcomes) in (2)(2)(2)(2)(1) ways (= 16 ways)

Answer: E

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: A coin with heads on one side and tails on the other has a 1/2 probabi  [#permalink]

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New post 03 Jan 2019, 10:04
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Bunuel wrote:
A coin with heads on one side and tails on the other has a 1/2 probability of landing on heads. If the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be heads? Outcomes are distinct if they do not contain exactly the same results in exactly the same order.

(A) 12
(B) 13
(C) 14
(D) 15
(E) 16


We need 5 flips of a fair coin such that

__ __ __ __ H

On each of the previous flips, we can have either Heads or Tails so there are 2 ways.

For the 4 previous flips then, there are 2*2*2*2 = 16 ways

Answer (E)
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Re: A coin with heads on one side and tails on the other has a 1/2 probabi  [#permalink]

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New post 03 Jan 2019, 23:40
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Can you please check OA Bunuel

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Re: A coin with heads on one side and tails on the other has a 1/2 probabi  [#permalink]

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New post 04 Jan 2019, 01:38
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Re: A coin with heads on one side and tails on the other has a 1/2 probabi   [#permalink] 04 Jan 2019, 01:38
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