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# Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze.

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Intern
Joined: 04 Jul 2018
Posts: 4
Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze.  [#permalink]

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26 Jan 2019, 21:59
2
2
00:00

Difficulty:

55% (hard)

Question Stats:

43% (02:24) correct 57% (02:11) wrong based on 18 sessions

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Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze. They all toss each of their coins once and record the results. Two results are the same if two gold coins land on the same face, two silver coins land on the same face, and two bronze coins land on the same face. What is the probability that Paul's result is the same as at least one of the other two results?

A. 15/32
B. 15/64
C. 31/64
D. 3/8
E. 1/2
Manager
Joined: 15 Feb 2018
Posts: 247
Re: Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze.  [#permalink]

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26 Jan 2019, 23:13
1
dreamerchaser, what is the question source?

It's very easy to get confused in this question.

Each coin can be heads or tails. Each person has 3 coins. So there are 8 combinations of results for each person $$(2^3)$$. We are not trying to find find when any of their combinations match, only when P matches Q or R.

I am answering for the 1-p, so the probability of P not matching Q or R.
P is guaranteed to get the result of P, so we can ignore it.

Q can get 7 combinations different to P's (7/8) and R can get 7 different combinations too (7/8) - remember, we don't have to find the combinations that P and Q don't have.

$$\frac{7}{8}·\frac{7}{8}=\frac{49}{64}$$
Is the probability that P won't match Q or R.

1-p is the probability that it will
$$\frac{64}{64}-\frac{49}{64}=\frac{15}{64}$$

B
Senior Manager
Joined: 28 Jul 2016
Posts: 250
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
Re: Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze.  [#permalink]

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27 Jan 2019, 03:32
still not sure if I understood the explanation.
Can any expert comment on it
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Intern
Joined: 04 Jul 2018
Posts: 4
Re: Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze.  [#permalink]

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27 Jan 2019, 08:45
Anyone can help to solve this question in an understandable way
Re: Paul, Quinn, and Richard each have 3 coins: Gold, Silver, and Bronze.   [#permalink] 27 Jan 2019, 08:45
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