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# After each throw of a red die, the face that shows is marked with a

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Math Expert
Joined: 02 Sep 2009
Posts: 50000
After each throw of a red die, the face that shows is marked with a  [#permalink]

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28 Jan 2018, 21:18
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Difficulty:

15% (low)

Question Stats:

84% (02:08) correct 16% (00:05) wrong based on 30 sessions

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After each throw of a red die, the face that shows is marked with a blue stripe. What is the probability that after 6 throws all faces of the die will be marked blue?

A. 3/126

B. 5/324

C. 4/216

D. 4/182

E. 5/216

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Re: After each throw of a red die, the face that shows is marked with a  [#permalink]

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28 Jan 2018, 21:40
B

Chances of marking a blue face on first throw=6/6. Whatever be the face we can mark it blue.
Similarly in second throw=5/6
Third throw=4/6
Fourth throw=3/6
Fifth throw=2/6
Sixth throw=1/6

Hence the total probability is 6/6*5/6*4/6*3/6*2/6*1/6= 5/324

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Re: After each throw of a red die, the top face is marked with a blue  [#permalink]

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29 Jan 2018, 06:53
Bunuel wrote:
After each throw of a red die, the top face is marked with a blue stripe. What is the probability that after 6 throws all faces of the die will be marked blue?

A. 3/126
B. 5/324
C. 1/54
D. 2/91
E. 5/216

After every throw, the top face of the red die is marked with a blue stripe. We are
asked to find the probability that all the 6 faces of the die are marked blue in the
first 6 throw(s)

This is possible when each and every throw yields a different number. The first throw
could yield any of the 6 digits. The second throw can be anything but the digit we get
in the first throw. Similarly, the third number could be any other digit except the digit
which we get in the first and second throws.

The probability is $$1*\frac{5}{6}*\frac{4*3}{6*6}*\frac{2}{6}*\frac{1}{6} = \frac{5}{6}*\frac{1}{3}*\frac{1}{3}*\frac{1}{6} = \frac{5}{324}$$(Option B)
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Re: After each throw of a red die, the top face is marked with a blue  [#permalink]

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29 Jan 2018, 06:56
Bunuel wrote:
After each throw of a red die, the top face is marked with a blue stripe. What is the probability that after 6 throws all faces of the die will be marked blue?

A. 3/126
B. 5/324
C. 1/54
D. 2/91
E. 5/216

Total Outcomes = 6^6 . (Cause any one of the six faces may appear on the top in each throw)

Favourable outcomes = 6*5*4*3*2*1 = 6! = 720 (Cause the top face shouldn't repeat hence there are 6 acceptable outcomes for the first throw and subsequently 5 acceptable as the face earlier obtained shouldn't repeat and so on...

Probability = 720/6^6 = 5/324

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Re: After each throw of a red die, the face that shows is marked with a  [#permalink]

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30 Jan 2018, 11:12
Bunuel wrote:
After each throw of a red die, the face that shows is marked with a blue stripe. What is the probability that after 6 throws all faces of the die will be marked blue?

A. 3/126

B. 5/324

C. 4/216

D. 4/182

E. 5/216

There is a 1/1 chance of rolling any number on the first roll, after which the side with that number is marked with blue. In the second roll, there is a 5/6 probability that a red side shows up; in the third roll, there is a 4/6 probability that a red side shows up, and so on. .

The total probability is:

1 x 5/6 x 4/6 x 3/6 x 2/6 x 1/6

1 x 5/6 x 2/3 x 1/2 x 1/3 x 1/6 = 10/648 = 5/324

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Re: After each throw of a red die, the face that shows is marked with a &nbs [#permalink] 30 Jan 2018, 11:12
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