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# A six-sided die with faces numbered one through six is rolled three ti

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Joined: 02 Nov 2016
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A six-sided die with faces numbered one through six is rolled three ti  [#permalink]

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14 Feb 2019, 01:31
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Difficulty:

5% (low)

Question Stats:

85% (01:10) correct 15% (01:53) wrong based on 61 sessions

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A six-sided die with faces numbered one through six is rolled three times. What is the probability that the face with the number 6 on it will NOT be facing upward on all three rolls?

A. 1/116
B. 1/6
C. 2/3
D. 17/18
E. 215/216

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A six-sided die with faces numbered one through six is rolled three ti  [#permalink]

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Updated on: 14 Feb 2019, 05:34
A six-sided die with faces numbered one through six is rolled three times. What is the probability that the face with the number 6 on it will NOT be facing upward on all three rolls?

A. 1/116
B. 1/6
C. 2/3
D. 17/18
E. 215/216

Probability on all three dice to not show 6 at the top of any throw = (5/6)*(5/6)*5/6) = 125/216

Probability on all three dice to not show 6 at the top of all the throws =1-(1/216) = 215/216

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Originally posted by GMATinsight on 14 Feb 2019, 04:32.
Last edited by GMATinsight on 14 Feb 2019, 05:34, edited 1 time in total.
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Re: A six-sided die with faces numbered one through six is rolled three ti  [#permalink]

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14 Feb 2019, 05:31
1
A six-sided die with faces numbered one through six is rolled three times. What is the probability that the face with the number 6 on it will NOT be facing upward on all three rolls?

A. 1/116
B. 1/6
C. 2/3
D. 17/18
E. 215/216

I am assuming the question means that 6 will not be on ALL rolls. So it could be on 1 or 2 rolls.
So 1, 6, 2 or 6, 6, 3 would be a valid combination.

The probability of 6 on ALL 3 rolls is (1/6)*(1/6)*(1/6) = 1/216
So the probability that we will NOT have 6s on ALL rolls = 1 - 1/216 = 215/216

The reason I am assuming that the question implies no 6 on all rolls but one or two are fine is because else it would be worded like this:
"... 6 will not be facing upward on ANY of the three rolls".
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Re: A six-sided die with faces numbered one through six is rolled three ti  [#permalink]

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14 Feb 2019, 09:44
A six-sided die with faces numbered one through six is rolled three times. What is the probability that the face with the number 6 on it will NOT be facing upward on all three rolls?

A. 1/116
B. 1/6
C. 2/3
D. 17/18
E. 215/216

probability that the face with the number 6 on it will NOT be facing upward on all three rolls

P of getting a 6 in all three rolls
1/6*1/6*1/6 = 1/216
and not getting a 6 = 1-1/216 = 215/216
IMO E
Re: A six-sided die with faces numbered one through six is rolled three ti   [#permalink] 14 Feb 2019, 09:44
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