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

Question

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

RaghavKhanna · Answer

Total number of outcomes = 6^3 = 216

Number of favourable outcomes = 4*4*4

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

Answer: D

Posted from my mobile device

GMATinsight · Answer

Answer: Option D

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

https://www.youtube.com/watch?v=rTCwvh5Roq8

Archit3110 · Answer

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

NitishJain · Answer

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}

azamatboden · Answer

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

BrushMyQuant · Answer

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!

Playlist on Solved Problems on Probability  here

Watch the following video to MASTER Dice Rolling Probability Problems

https://www.youtube.com/watch?v=5PVZYQXet18

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards