Question

What is the probability of getting a sum of 8 or 14 when rolling 3 dice simultaneously?

Answer 1

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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]