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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] New post 30 Jul 2018, 10:56
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78% (00:55) correct 21% (00:42) wrong based on 46 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
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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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Retired Moderator
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Joined: 07 Jun 2014
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Followers: 171

Kudos [?]: 2934 [0], given: 394

Re: A certain coin with heads on one side and tails on the other [#permalink] New post 09 Aug 2018, 14:29
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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] New post 16 Jul 2019, 15:54
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 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) \(\frac{2}{3}\)



Easy way:

Let's examine ONE case in which we get exactly 2 tails: HTT

P(HTT)=\(\frac{1}{2}\) *\(\frac{1}{2}\)*\(\frac{1}{2}\)=\(\frac{1}{8}\)

This, of course, is just ONE possible way to get exactly 2 TAILS.

Another possible outcome is THT

Here, P(THT)= (\(\frac{1}{2}\))(\(\frac{1}{2}\))(\(\frac{1}{2}\)) =\(\frac{1}{8}\)

As you might guess, each possible outcome will have the same probability (\(\frac{1}{8}\)). So, the question becomes "In how many different ways can we get exactly 2 TAILS ?"

In other words, in how many different ways can we arrange the letters HTT?\(\frac{3!}{2!}\)=3 WAY.

So P(exactly 2 Tails) = (\(\frac{1}{8}\))(3) = \(\frac{3}{8}\)
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Re: A certain coin with heads on one side and tails on the other   [#permalink] 16 Jul 2019, 15:54
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