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805+ (Hard)|   Probability|      
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Bunuel
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Each face of a cube is given a single narrow stripe painted from the 29 Mar 2019, 01:39
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95% (hard)

Question Stats:

32% (02:20) correct 68% (01:57) wrong based on 90 sessions

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Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. The choice of the edge pairing is made at random and independently for each face. What is the probability that there is a continuous stripe encircling the cube?

(A) 1/8
(B) 3/16
(C) 1/4
(D) 3/8
(E) 1/2
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B
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Each face of a cube is given a single narrow stripe painted from the 29 Mar 2019, 09:00
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Bunuel
Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. The choice of the edge pairing is made at random and independently for each face. What is the probability that there is a continuous stripe encircling the cube?

(A) 1/8
(B) 3/16
(C) 1/4
(D) 3/8
(E) 1/2
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total pairs of 6 sided cube ; 3 and total faces = 8
3/8 is P of having stripe
IMO D

P.S I am not sure of answer here..
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Each face of a cube is given a single narrow stripe painted from the Updated on: 19 Apr 2019, 20:54
Originally posted by Ypsychotic on 29 Mar 2019, 19:38.
Last edited by Ypsychotic on 19 Apr 2019, 20:54, edited 1 time in total.
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Each face of a cube is given a single narrow stripe painted from the center of one edge to the center of the opposite edge. The choice of the edge pairing is made at random and independently for each face. What is the probability that there is a continuous stripe encircling the cube?

(A) 1/8
(B) 3/16
(C) 1/4
(D) 3/8
(E) 1/2
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Let the cube be ABCDEFGH.

For each face, there will be two strips. Lets first consider the encircling part, for that remove opposite two faces, and consider the rest of the four faces. eg. consider ABCD, CDEF, EFGH, GHBA, and don't consider ABEF and CDGH. For this portion, there will be only one time, when the strip will encircle the cube. and for each face, there will be two strips.

So, Probability for the strip to encircle the cube for this portion=\(\frac{1}{(2c1)^4}=\frac{1}{16}\)

There will be three such protions, in total the probability is 3/16.

IMO, Option B.
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File comment: Blue part is the portion considered, white part is not considered. 3 such parts will be there, removing each pair of opposite faces.
Untitled.jpg
Untitled.jpg [ 8.08 KiB | Viewed 4634 times ]

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Each face of a cube is given a single narrow stripe painted from the 29 Mar 2019, 23:01
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Ypsychotic
Let the cube be ABCDEFGH.

For each face, there will be two strips. Lets first consider the encircling part, for that remove opposite two faces, and consider the rest of the four faces. eg. consider ABCD, CDEF, EFGH, GHBA, and don't consider ABEF and CDGH. For this portion, there will be only one time, when the strip will encircle the cube. and for each face, there will be two strips.
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Can you explain why there would be two strips per face?
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Each face of a cube is given a single narrow stripe painted from the 30 Mar 2019, 19:17
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OhsostudiousMJ
Ypsychotic
Let the cube be ABCDEFGH.

For each face, there will be two strips. Lets first consider the encircling part, for that remove opposite two faces, and consider the rest of the four faces. eg. consider ABCD, CDEF, EFGH, GHBA, and don't consider ABEF and CDGH. For this portion, there will be only one time, when the strip will encircle the cube. and for each face, there will be two strips.

Can you explain why there would be two strips per face?
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Beause it is mentioned in the question that a strip is formed by joining it from the center of first edge to opposite edge. As there are four edges in a face, with two pairs opposite to each other. For instance, in the face abcd, One strip would from ab to cd, other from ad to bc. Hence, two strips.
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Each face of a cube is given a single narrow stripe painted from the 31 Mar 2019, 21:08
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Ypsychotic


Beause it is mentioned in the question that a strip is formed by joining it from the center of first edge to opposite edge. As there are four edges in a face, with two pairs opposite to each other. For instance, in the face abcd, One strip would from ab to cd, other from ad to bc. Hence, two strips.
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Okay, thanks, but I still got a question unanswered..
In your previous post, the answer to the question,
Ypsychotic
So, Probability for the strip to encircle the cube for this portion \(\frac{1}{(2c1)∗(4c1)}\)=\(\frac{1}{16}\)
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Shouldn't the answer be 1/8?
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Each face of a cube is given a single narrow stripe painted from the 19 Apr 2019, 20:53
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OhsostudiousMJ
Ypsychotic


Beause it is mentioned in the question that a strip is formed by joining it from the center of first edge to opposite edge. As there are four edges in a face, with two pairs opposite to each other. For instance, in the face abcd, One strip would from ab to cd, other from ad to bc. Hence, two strips.

Okay, thanks, but I still got a question unanswered..
In your previous post, the answer to the question,
Ypsychotic
So, Probability for the strip to encircle the cube for this portion \(\frac{1}{(2c1)∗(4c1)}\)=\(\frac{1}{16}\)

Shouldn't the answer be 1/8?
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You're right. I wrote it wrong. It should be \(\frac{1}{2c1*2c1*2c1*2c1}=\frac{1}{16}\) because for every strip on one face there are two strips on another face. So, in total, there are 2*2*2*2=16 combinations with only one combination when it encircles it. So, only once when each strip will be the one in alignment, it will encircle the cube. So, Probability=\(\frac{1}{16}\). Hope it helps.
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Each face of a cube is given a single narrow stripe painted from the 22 Jul 2023, 01:23
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