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If a fair six-sided die is rolled three times, what is the probability

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Bunuel
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If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   06 Jul 2020, 00:39
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If a fair six-sided die is rolled three times, what is the probability that neither a 2 nor a 4 will show up on any roll?

A. 1/36
B. 1/27
C. 1/6
D. 8/27
E. 2/3
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D
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Re: If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   06 Jul 2020, 00:46
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Total number of outcomes = 6^3 = 216

Number of favourable outcomes = 4*4*4

Probability = 64/216 = 16/54 = 8/27

Answer: D

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Re: If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   06 Jul 2020, 01:42
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Bunuel wrote:
If a fair six-sided die is rolled three times, what is the probability that neither a 2 nor a 4 will show up on any roll?

A. 1/36
B. 1/27
C. 1/6
D. 8/27
E. 2/3



Answer: Option D

Please check teh step-by-step video explanation as mentioed below



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If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   Updated on: 06 Jul 2020, 12:55
P of not getting either 2 or 4 ; left with 1,3,5,6 ; 4/6 ways ; 2/3 ways and when thrown thrice it would become

(2/3)^3 ; 8/27

OPTION D ;

OTHER WAY

total ways of not getting 2 or 4 ; we get 1,3,5,6 ; 4 ways ; when done thrice ; 4*4*4 ;64
and total chances of throwing dice thrice ; 6*6*6 ; 216
P ; 64/216 ; 8/27
OPTION D

Bunuel wrote:
If a fair six-sided die is rolled three times, what is the probability that neither a 2 nor a 4 will show up on any roll?

A. 1/36
B. 1/27
C. 1/6
D. 8/27
E. 2/3

Originally posted by Archit3110 on 06 Jul 2020, 02:13.
Last edited by Archit3110 on 06 Jul 2020, 12:55, edited 1 time in total.
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If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   06 Jul 2020, 12:52
IMO D


Probability(neither a 2 nor a 4 will show) = P(neither a 2 nor a 4 will show on first roll) * P(neither a 2 nor a 4 will show on second roll) * P(neither a 2 nor a 4 will show on third roll)

Probability(neither a 2 nor a 4 will show) = \(\frac{4}{6}\) *\(\frac{4}{6}\)* \(\frac{4}{6}\) = \(\frac{8}{27}\)
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Re: If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   07 Jul 2020, 11:21
I think the easiest way is just to deselect the restrictions. If you don't want 2 or 4 to roll out, then you've got 4 options.

If you throw a dice 3 times --> 4 x 4 x 4
Total possibilities --> 6 x 6 x 6
Probability: (4x4x4)/(6x6x6)=2^3/3^3=8/27
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Re: If a fair six-sided die is rolled three times, what is the probability [#permalink] New post   13 Oct 2022, 10:37
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Given that a fair 6-sided die is rolled three times and We need to find what is the probability that neither a 2 nor a 4 will show up on any roll?

As we are rolling three dice => Number of cases = \(6^3\) = 216

In each toss we need to get any number apart from 2 or 4 => For each toss there are 4 favorable outcomes out of 6. (Getting a 1, 3, 5, 6)

=> Probability of getting neither a 2 nor a 4 in one toss = \(\frac{4}{6}\) = \(\frac{2}{3}\)

=> Probability of getting neither a 2 nor a 4 in any of the three tosses = \(\frac{2}{3}\) * \(\frac{2}{3}\) * \(\frac{2}{3}\) = \(\frac{8}{27}\)

So, Answer will be D
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

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Re: If a fair six-sided die is rolled three times, what is the probability [#permalink]
13 Oct 2022, 10:37
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