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

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GMAT Club Legend
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Joined: 07 Jun 2014
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A certain coin with heads on one side and tails on the other [#permalink] New post 30 Jul 2018, 10:56
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Question Stats:

66% (01:00) correct 33% (00:32) wrong based on 9 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 three times, what is the probability of flipping 2 tails and 1 head, in any order?

(A) \(\frac{1}{8}\)
(B) \(\frac{1}{3}\)
(C) \(\frac{3}{8}\)
(D) \(\frac{5}{8}\)
(E) \(\frac{2}{3}\)
[Reveal] Spoiler: OA

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Re: A certain coin with heads on one side and tails on the other [#permalink] New post 31 Jul 2018, 07:19
It could be T H T, H T T or T T H

In each of the case the probability would be \(\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}\)
For 3 instances it would be \(\frac{3}{8}\)
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GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1613 [0], given: 375

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Re: A certain coin with heads on one side and tails on the other [#permalink] New post 09 Aug 2018, 14:29
Expert's post
Explanation

There are only 2 possible outcomes for each flip and only 3 flips total. The most straightforward approach is to list all of the possible outcomes: {HHH, HHT, HTH, HTT, TTT, TTH
THH, THT}.

Of these 8 possibilities, 3 of the outcomes have one head and two tails, so the probability of this event is \(\frac{3}{8}\).

Alternatively, count the total number of ways of getting 1 head without listing all the possibilities. If the coin is flipped 3 times and you want only 1 head, then there are 3 possible positions for the single head: on the first flip alone, on the second flip alone, or on the third flip alone. Since there are 2 possible outcomes for each flip, heads or tails, there are (2)(2)(2) = 8 total outcomes. Again, the probability is \(\frac{3}{8}\).
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Re: A certain coin with heads on one side and tails on the other   [#permalink] 09 Aug 2018, 14:29
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A certain coin with heads on one side and tails on the other

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