What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?
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GMAT Club Forum Index Problem Solving (PS)
What is the probability of getting a sum of 8 or 14 when : Problem Solving (PS)
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Difficulty: 700-Level
Topic Discussion
Page 1 of 2
1 2
gayathri Nov 26, 2004
00:00 ABCDE
DIFFICULTY: 95% (hard) QUESTION STATS: based on 554 sessions
32% (03:25) correct
68% (03:03) wrong
What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?
A. 1/6
B. 1/4
C. 1/2
D. 21/216
E. 32/216
Spoiler: OA
Kudos 9 kudos, 39 bookmarks
Most Helpful Community Reply
Richie Weasel Nov 26, 2004
"Gayathri"
What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?
a) 1/6
b) 1/4
c) 1/2
d) 21/216
e) 32/216
Is there a shorter way to do this than listing each possibility?
I am confident that there is a better way, but I looked at the first few possibilities
throw a 3 - 1 way
throw a 4 - 3 ways
throw a 5 - 6 ways
throw a 6 - 10 ways
and recognized these as triangular numbers (the series could also be identified as add 2, add 3, add 4 ...).
from there it was easy to calculate that there are 21 ways to hit an 8 and 15 ways to hit a 14. (Problems with fair dice and coins produce symmetrical probability distributions, so one can count down from 1 way to throw an 18)
[more than 2 minutes - less than 3 minutes]