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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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00:00

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.

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]
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.

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. _________________

greprepclubot

Re: A certain coin with heads on one side and tails on the other
[#permalink]
30 Oct 2019, 20:48