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

Redeem

Probability

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

Probability

by knight247 » Thu Sep 29, 2011 11:58 am
if x^2 + y^2 = r^2 is the equation of the circle with centre as origin and radius as r.

Point (P,Q) is randomly selected inside the above circle. What is the probability that P>Q>0 ?

OA [spoiler]1/8[/spoiler]
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pm
Location: Austin, TX
Thanked: 236 times
Followed by:54 members
GMAT Score:770

by GmatMathPro » Thu Sep 29, 2011 12:13 pm
Draw the graph of the circle in the coordinate plane and draw the line y=x. We want to know the probability that both the x and y coordinates are positive and the x-coordinate is greater than the y-coordinate. Only the points in the first quadrant have their x and y coordinates both positive, and only the points to the RIGHT of the line y=x have bigger x-coordinates than y-coordinates. If you draw the picture it's really easy to see that this is 1/8 of the circle.
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Thu Sep 29, 2011 12:25 pm
Hey Pete,
Thanks for ur response Bro. But what about a point in the 4th quadrant? Any point in the 4th quadrant would have +ve x coordinate and -ve y coordinate. So wouldn't that also count as x>y?
Top
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pm
Location: Austin, TX
Thanked: 236 times
Followed by:54 members
GMAT Score:770

by GmatMathPro » Thu Sep 29, 2011 12:27 pm
Yes, but remember we want points (P,Q) with P>Q>0, which means P and Q are BOTH positive. In the 4th quadrant only P would be positive, but Q would be negative.
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Thu Sep 29, 2011 12:30 pm
Whoops..Ur right bro. I overlooked the >0 part. A light bulb just lit over my head...just like in ur profile pic...lolzzz...Thanks
Top
User avatar
GMAT Instructor
Posts: 349
Joined: Wed Sep 28, 2011 3:38 pm
Location: Austin, TX
Thanked: 236 times
Followed by:54 members
GMAT Score:770

by GmatMathPro » Thu Sep 29, 2011 12:43 pm
Haha. Happy to help, my man.
Pete Ackley
GMAT Math Pro
Free Online Tutoring Trial
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Sep 29, 2011 1:25 pm
For an illustrated solution to a very similar problem, check here:

https://www.beatthegmat.com/probability-t90694.html
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1