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

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
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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:

100% (00:54) correct 0% (00:00) wrong based on 5 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 heads? 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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Sandy
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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 [0], given: 397

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

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