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# A certain coin with heads on one side and tails on the other

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A certain coin with heads on one side and tails on the other [#permalink]  05 Aug 2018, 14:29
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Question Stats:

87% (00:52) correct 12% (01:41) wrong based on 24 sessions
A certain coin with heads on one side and tails on the other has a $$\frac{1}{2}$$ probability of landing on heads. If the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be head?

Outcomes are distinct if they do not contain exactly the same results in exactly the same order.

[Reveal] Spoiler: OA
16

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Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 175

Kudos [?]: 3033 [0], given: 394

Re: A certain coin with heads on one side and tails on the other [#permalink]  07 Aug 2018, 16:51
Expert's post
Explanation

This problem utilizes the fundamental counting principle, which states that the total number of choices is equal to the product of the independent choices. For the first flip, there are 2 options: heads or tails.

Similarly, for the second flip, there 2 options; for the third, there are 2 options; for the fourth, there are 2 options; and for the fifth there is only one option because the problem restricts this final flip to heads. Therefore, the total number of outcomes is (2)(2)(2)(2)(1) = 16. A good rephrasing of this question is, “How many different outcomes are
there if the coin is flipped 4 times?” The fifth flip, having been restricted to heads, is irrelevant.

Therefore, the total number of ways to flip the coin five times with heads for the fifth flip is equal to the total number of ways to flip the coin four times; either way, the answer is 16.
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Re: A certain coin with heads on one side and tails on the other [#permalink]  14 Jul 2019, 21:37
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the last flip must be head(S) - this plural confused me .
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Re: A certain coin with heads on one side and tails on the other [#permalink]  04 Oct 2019, 14:18
16
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Re: A certain coin with heads on one side and tails on the other [#permalink]  18 Oct 2019, 05:46
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sandy wrote:
A certain coin with heads on one side and tails on the other has a $$\frac{1}{2}$$ probability of landing on heads. If the coin is flipped 5 times, how many distinct outcomes are possible if the last flip must be head?

Outcomes are distinct if they do not contain exactly the same results in exactly the same order.

[Reveal] Spoiler: OA
16

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

Stage 1: Select an outcome for flip #1
There are 2 possible outcomes: heads or tails
So, we can complete stage 1 in 2 ways

Stage 2: Select an outcome for flip #2
There are 2 possible outcomes: heads or tails
So, we can complete stage 2 in 2 ways

Stage 3: Select an outcome for flip #3
We can have heads or tails. So, we can complete stage 3 in 2 ways

Stage 4: Select an outcome for flip #4
We can have heads or tails. So, we can complete stage 4 in 2 ways

Stage 5: Select an outcome for flip #5
So, we can complete stage 5 in 1 way

By the Fundamental Counting Principle (FCP), we can complete all 5 stages in (2)(2)(2)(2)(1) ways (= 16 ways)

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

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Re: A certain coin with heads on one side and tails on the other [#permalink]  30 Oct 2019, 20:48
This problem utilizes the fundamental counting principle, which states that the total number of choices is equal to the product of the independent choices. For the first flip, there are 2 options: heads or tails.

Similarly, for the second flip, there 2 options; for the third, there are 2 options; for the fourth, there are 2 options; and for the fifth there is only one option because the problem restricts this final flip to heads. Therefore, the total number of outcomes is (2)(2)(2)(2)(1) = 16. A good rephrasing of this question is, “How many different outcomes are
there if the coin is flipped 4 times?” The fifth flip, having been restricted to heads, is irrelevant.

Therefore, the total number of ways to flip the coin five times with heads for the fifth flip is equal to the total number of ways to flip the coin four times; either way, the answer is 16.
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Re: A certain coin with heads on one side and tails on the other   [#permalink] 30 Oct 2019, 20:48
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