BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Probablity - Die

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 70
Joined: Wed Feb 03, 2010 5:21 pm
GMAT Score:720

Probablity - Die

by skalevar » Tue Sep 07, 2010 6:47 pm
What is the probability of getting exactly 2 sixes on three rolls of a fair six sided die?

Can someone please provide an answer and explanation to the questions above? From Veritas Prep: Probability & Combinatorics.

(Answer is 5/72)



I got as far as # Total Outcomes = 6*6*6 =216, but I can't see how to find the # of favourable outcomes. Any insights you can give are much appreciated.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3650
Joined: Wed Jan 21, 2009 4:27 am
Location: India
Thanked: 267 times
Followed by:80 members
GMAT Score:760

by sanju09 » Tue Sep 07, 2010 7:53 pm
skalevar wrote:What is the probability of getting exactly 2 sixes on three rolls of a fair six sided die?

Can someone please provide an answer and explanation to the questions above? From Veritas Prep: Probability & Combinatorics.

(Answer is 5/72)



I got as far as # Total Outcomes = 6*6*6 =216, but I can't see how to find the # of favourable outcomes. Any insights you can give are much appreciated.
Given that two of the rolls show up a SIX, the remaining single roll can show up 5 possibilities other than a SIX, and those 5 possibilities could be assigned to any of the 3 rolls of die; a total of 5 × 3 ways favor the required event out of a total of 6 × 6 × 6 number of ways.

Required probability = (5 × 3)/ (6 × 6 × 6) = [spoiler]5/72[/spoiler]
The mind is everything. What you think you become. -Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pm
Location: Milpitas, CA
Thanked: 447 times
Followed by:88 members

by Rahul@gurome » Tue Sep 07, 2010 7:54 pm
Solution:
Probability of having a six on a single roll of a die is 1/6.
Probability that there is no six on a single roll of die is 5/6.
0r probability of only 2 sixes in three rolls of die is (1/6)*(1/6)*(5/6) = 5/216. Here we multiply by 5/6 because one of the three rolls have to be without 6.
Number of ways of having only 2 sixes in three rolls of a die is 3C2 = 3.

So required probability is 3*(5/216) = 5/72.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Post new topic Post Reply
• Page 1 of 1