What is the probability of rolling three fair...

This topic has expert replies
Legendary Member
Posts: 2218
Joined: Sun Oct 29, 2017 2:04 pm
Followed by:6 members
What is the probability of rolling three fair dice and having all three dice show an odd number?

A. 5/8
B. 1/8
C. 1/36
D. 1/108
E. 1/216

The OA is B.

I need help to solve this PS question. Please, can any expert assist me with it? Thanks.

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Nov 01, 2017 12:28 pm
Hi swerve,

We're asked for the probability of rolling three fair 6-sided dice and having all three dice show an ODD number.

The six numbers on a die are 1, 2, 3, 4, 5 and 6 - half of those numbers are odd and half are even.

The probability of rolling an ODD number on each die is 3/6 = 1/2
The probability of rolling ODD numbers on ALL 3 dice is (1/2)(1/2)(1/2) = 1/8

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Thu Nov 02, 2017 8:25 am
swerve wrote:What is the probability of rolling three fair dice and having all three dice show an odd number?

A. 5/8
B. 1/8
C. 1/36
D. 1/108
E. 1/216
Each die has 6 possible outcomes (1, 2, 3, 4, 5, 6)
Of those outcomes, 3 are ODD (1, 3, 5)
So, when we role ONE die, P(ODD) = 3/6 = 1/2

P(all 3 dice are odd) = P(1st roll is odd AND 2nd roll is odd AND 3rd roll is odd)
= P(1st roll is odd) x P(2nd roll is odd) x P(3rd roll is odd)
= 1/2 x 1/2 x 1/2
= 1/8

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Fri Nov 01, 2019 6:54 pm
swerve wrote:What is the probability of rolling three fair dice and having all three dice show an odd number?

A. 5/8
B. 1/8
C. 1/36
D. 1/108
E. 1/216

The OA is B.

I need help to solve this PS question. Please, can any expert assist me with it? Thanks.
Since the probability of a die showing an odd number is ½, the probability of all three dice showing an odd number is 1/2 x 1/2 x 1/2 = 1/8.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage