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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]  30 Jul 2018, 10:56
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Question Stats:

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]  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
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 171

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

Re: A certain coin with heads on one side and tails on the other [#permalink]  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]  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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