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# What is the probability of flipping a fair coin three times and the co

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What is the probability of flipping a fair coin three times and the co [#permalink]

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22 Dec 2010, 06:20
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What is the probability of flipping a fair coin three times and the coin landing on heads on exactly two flips?

A. 3/8
B. 5/8
C. 7/8
D. 1/8
E. 1/4
[Reveal] Spoiler: OA

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Last edited by Bunuel on 29 Mar 2017, 20:32, edited 1 time in total.
Renamed the topic and edited the question.
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Posts: 43917
Re: What is the probability of flipping a fair coin three times and the co [#permalink]

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22 Dec 2010, 06:25
Expert's post
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rxs0005 wrote:
What is the probability of flipping a fair coin three times and the coin landing on heads on exactly two flips?

3/8
5/8
7/8
1/8
1/4

$$P(H=2)=\frac{3!}{2!}*\frac{1}{2^3}=\frac{3}{8}$$, multiplying by 3!/2! as the case of 2 heads out of 3 tries can occur in 3 ways: HHT, HTH, THH - # of permutation of 3 letters out of which 2 are identical.

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Re: What is the probability of flipping a fair coin three times and the co [#permalink]

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02 Jan 2011, 02:10
1
KUDOS
Probability = (Favorable combination)/(Total combination)

Favorable combination = (HHT, HTH, THH) ==> 3

Total combination = 8 (2^3)

Probability = (3)/(8)

(A)
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Re: What is the probability of flipping a fair coin three times and the co [#permalink]

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29 Mar 2017, 11:52
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Re: What is the probability of flipping a fair coin three times and the co [#permalink]

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04 Apr 2017, 15:01
rxs0005 wrote:
What is the probability of flipping a fair coin three times and the coin landing on heads on exactly two flips?

A. 3/8
B. 5/8
C. 7/8
D. 1/8
E. 1/4

We can assume the first 2 flips are heads (H) and the last flip is tails (T). Thus:

P(H-H-T) = 1/2 x 1/2 x 1/2 = 1/8

However, we need to determine in how many ways we can get 2 heads and 1 tails. That number will be equivalent to how many ways we can organize the letters H-H-T.

We use the indistinguishable permutations formula to determine the number of ways to arrange H-H-T: 3!/2! = 3 ways. (Note: The 3 ways are H-H-T, H-T-H, and T-H-H.)

Each of these 3 ways has the same probability of occurring. Thus, the total probability is:

1/8 x 3 = 3/8

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Re: What is the probability of flipping a fair coin three times and the co [#permalink]

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05 Apr 2017, 19:19
1
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Expert's post
Hi All,

This question can be solved simply by listing out the possibilities and answering the exact question that is asked.

Since we're flipping a coin 3 times, there are only (2)(2)(2) = 8 possible outcomes. They are...

HHH
HHT
HTH
THH

TTT
TTH
THT
HTT

We're asked for the probability of getting exactly 2 HEADS from those 3 tosses. There are three ways (out of 8 total) to get exactly 2 heads (HHT, HTH and THH).

[Reveal] Spoiler:
A

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Re: What is the probability of flipping a fair coin three times and the co   [#permalink] 05 Apr 2017, 19:19
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